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Arch. lib. 


9 


NA2i:21 
S45 


Arch.  Lib. 


129734 


PERMANENT  RESERVE 


i>^i 


S  H  AWS 

CIVIL    ARCHITECTURE; 

BEING 

A   COMPLETE   THEORETICAL   AND   PRACTICAL 

SYSTEM     OF     BUILDING, 


CONTAINING 


THE    FUNDAMENTAL   PRINCIPLES    OF    THE   ART, 


ILLUSTRATED   BY   EIGHTY-TWO    COPPERPLATE   ENGRAVINGS. 


By   EDWARD    SHAW,  Architect. 


SIXTH    EDITION,    REVISED    AND    IMPROVED. 

TO    WHICH    AEE   ADDED 

TWENTY   COPPERPLATE   ENGRAVINGS, 

ALSO, 

A   TREATISE   ON   GOTHIC   ARCHITECTURE,  WITH  PLATES,  &c 

BY  THOMAS  W.  SILLOWAY  AND  GEORGE  M.  HARDING, 

AKCHITECTS. 


BOSTON : 

PUBLISHED    BY    JOHN    P.   JEWETT    AND    COMPANY 

CLEVELAND,  OHIO :  JEWETT,  PROCTOR,  AND  WORTHINGTON. 

MDCCCLII. 


Entered  according  to  act  of  Congress,  in  tlie  year  1859,  by 

LUTHER    STEVENS, 

In  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


ADYERTISEMENT 

TO    THE    FIRST    EDITION. 


It  is  obvious  that  most  writers  on  CivU  Architecture  have  not  entered  into  those  mathematical 
principles  on  which  this  noble  art  ultimately  rests,  and  from  which  it  derives  its  very  existence. 
They  may  rather  be  said  to  consider  it  merely  as  an  art  than  as  a  science  also,  and  are  more  cal- 
culated to  instruct  the  student  in  dra-\ving  architectiu'al  plans  than  to  point  out  and  elucidate 
those  imalterable  rules  and  first  principles  which,  however  unperceived,  (as  Mr.  Nicholson  justly 
observes,)  must  enter  into  the  very  essence  of  every  plan  that  is  correct  and  practicable. 

The  student,  in  the  outset,  should  commence  his  inquiry  by  going  back  to  the  most  simple 
elements  of  mathematical  knowledge,  there  to  obtain  the  real  clew  to  his  future  studies,  and  from 
thence,  gradually  and  scientifically,  to  proceed  to  more  complex  problems  and  more  diversified 
plans.  On  this  principle  is  founded  the  superior  skUl  of  the  Grecian  and  Eoman  artists,  which 
has,  as  yet,  been  mirivalled. 

We  should  not  content  ourselves  by  merely  drawing  from  their  works,  and  then  superadding 
the  invention  of  our  ovm  imagination ;  but  we  should  continually  recur  to  the  ground  on  which 
they  trod,  and  make  that  the  criterion  of  all  our  attempts.  It  is  principally  to  assist  the  practical 
mechanic,  as  well  as  the  student,  that  this  work  has  been  projected ;  and,  as  will  appear,  much 
pains  have  been  taken  to  lay  down  the  fundamental  principles  of  architectiu'e  m  a  clear,  distinct, 
and  intelligible  manner,  and  to  apply  the  whole  to  practice  by  plain  and  obvious  examples  and 
illustrations.  I  have  endeavored  to  arrange  the  contents  so  as  to  be  useful  to  the  student,  as  well 
as  to  all  classes  of  operative  builders. 

Those  workmen,  therefore,  Avho  aspire  to  any  degree  of  superiority  and  taste  in  either  of  these 
branches,  will  be  able  from  hence,  by  improving  their  leisure  hours,  in  a  short  time  to  understand 
the  principles  of  theu-  respective  occupations,  and  to  execute  with  taste  and  pleasure  what  they  do 
now  but  mechanically. 

In  this  work  is  given  whatever  the  experience  of  the  most  judicious  professors  has  sanctioned 
as  the  best  mode  of  affecting  their  professional  purposes,  with  the  reasons  on  which  that  preference 
is  founded.  To  this  are  added  examples  both  of  Grecian  and  Roman  antiquities,  and  remarks  on 
the  beauties  of  each.  Particular  attention  is  paid  to  the  theory  of  shadows,  both  from  dhcct  and 
reflected  light,  and  examples  adduced  of  the  relative  degrees  of  light  and  shade  on  different  sur- 
faces, variously  inclined  to  the  luminary  and  the  eye.  Also,  a  select  set  of  problems  are  di'awn 
from  Nicholson's  writings,  entirely  new,  and  all  ultimately  connected  with  the  subject  in  hand. 


lJc9784 


4  ADVERTISEMENT. 

They  are  disposed  in  methodical  order,  and  are  preceded  by  the  necessary  definitions.  It  is  not 
intended  by  this  part  wholly  to  set  aside  the  study  of  Euclid  and  authors  who  have  written  on 
Conic  Sections.  An  attentive  perusal  of  their  works  will  always  amply  repay  the  student's 
trouble. 

When  the  vast  importance  and  utility  of  Geometry  are  considered,  the  student  will  never  regret 
any  pains  he  may  take  to  make  himself  thoroughly  master  of  every  part  of  it.  Particular  atten- 
tion has  been  paid  to  ellipses  and  curves  —  the  problems  relating  to  which  will  be  found  par- 
ticularly useful  in  describing  elliptical  and  Gothic  arches,  finding  their  joints,  and  describing 
mouldings  of  every  degree  of  cru'vature,  under  various  circimistances,  with  Conic  Sections ;  also, 
the  Sections  of  Solids,  a  thorough  acquaintance  with  them  being  absolutely  necessary  for  under- 
standing the  theory  and  disposition  of  shadows,  the  explanation  of  which  will  be  highly  gratifying 
to  every  scientific  reader. 

In  view  of  the  present  taste  for  architectural  knowledge,  and  the  inadequacy  of  means  to 

obtain  that  science,  arising  from  the  costly  and  voluminous  works  on  the  subject,  I  have  been 

chiefly  induced  to  compile  a  work  of  this  kind.     Being  fully  convinced  of  its  utility,  from  very 

arduous  research  into  its  constituent  principles,  from  my  early  apprenticeship  to  the  present 

time, — having  had  more  than  twenty  years' practice  in  the  art  of  building,  —  I  have  brought 

together  the  following  system  in  a  concise  but  intelligible  manner,  Avhich  consists  principally  of 

extracts  from  Vitruvius,  Stuart,  Chambers,  Nicholson,  and  other  authors  of  eminence.     If  I  have 

made  a  judicious  arrangement  of  the  several  subjects,  I  have  accomplished  all  I  anticipated ;  and 

under  these  considerations,  therefore,  I  submit  this  work  to  the  public  for  their  approbation  and 

patronage. 

EDWARD     SHAW. 


ADYEETISEMENT 

TO    THE    SIXTH    EDITION. 


Being  encouraged  by  the  rapid  and  extensive  sale  of  the  five  former  editions  of  this  work,  and 
the  urgent  calls  made  in  consequence  of  its  having  been  out  of  print  for  several  years,  I  have  been 
induced  by  the  advice  of  my  friends  to  secure  the  valuable  services  of  Messrs.  SUloway  and 
Harding,  architects  of  Boston,  gentlemen  well  versed  in  the  science  they  profess,  to  assist  in 
revising  the  fifth  edition,  and  prepare  additional  di-awings  for  a  sixth,  which  has  resulted  in  the 
exclusion  of  several  of  the  old  plates,  and  the  substitution  of  twenty  new  ones  of  a  character  in 
keeping  with  the  improvements  of  the  day,  and  of  great  practical  use  to  the  carpenter  and 
builder,  among  which  are  four  plates  of  Gothic  details  selected  from  Pugin,  one  of  the  best  of  the 
English  authors  on  this  subject. 

The  sixth  edition,  thus  improved  and  enlarged,  I  now  offer  for  the  attention  and  patronage  of 

an  enlightened  public. 

EDWARD    SHAW. 
Januaky  1,  1852. 


CONTENTS. 


PAGE  PLATE 

INTRODUCTION.  9 

Construction  of  Houses, 17 

Doors  and  Windows, 18 

Mouldings, 22 

To  draw  Volutes,  Columns,  and  Cornices, 22,  23 

Construction  of  Bridges, 27 

Wooden  Bridges, 32 

Iron  Bridges, 33 

Western  Avenue, 34 

Warren  Bridge, 34 

PRACTICAL  GEOMETRY. 

Definition  of  Lines  and  Points, 37  1 

Circles, 38  2 

Problems  on  Points  and  Lines 39  2,  3 

Trapeziums, 43  4 

CONIC   SECTIONS. 

Definitions, 45  5 

Ellipses, 46  (i 

Conjugates, 47  7 

To  describe  Ellipses, 48  8 

The  Parabola, 49  9 

Hyperbola 50  10 

To  describe  a  Conic  Section, 51  11 

Sections  of  Solids, 52  12 

Sections  of  a  Cone, 53  12,  13 

Cycloid  or  Epicycloid, 56  13 

Section   of  Planes, 56  14 

Application  of  the  Trihedral, 57  14 

Principles  of  Projection, 59  15 

Development  of  tlie  Surfaces  of  Solids, 59  15 

Projections  of  Prisms, 64  16 

SHADOWS. 

Efiect  of  Distance, 66 

Seat  of  the  Sun's  Rays, 67  17 

Upright  Prisms, 68  18 

Polygonal  Ring, 69  19 

Elevation  of  a  Circular  Ring, 70  19 

Lines  of  Light  and  Shade  on  a  Sphere, 71  20 


PAGE    PLATE 

Lines  of  Light  and  Shade  from  the  Abacus  of  a 

Cylinder,  71  20 

Light  and  Shade  on  a  Prism, 72  21 

ESect  of  do.  on  Mouldings, 73  22 

Base  and  Capital, 77  23,  24 

Of  a  Cylmdrical  Recess, 78  25 

A  Hemisphere, 78  25 

MOULDINGS. 

Definitions, 79 

Roman  Mouldings, 80  26 

Modem         "         82  27 

Grecian         «         82  28,29 

Architraves, 83  30 

ORDERS. 

Tuscan  Order  of  Vitruvius, 84  31 

Modern  Tuscan  Order, 84  32 

ROMAN  DORIC. 

Example  by  Palladio, 85  33 

Example  from  the  Diocletian  Baths, 86  34 

Roman  Doric,  as  approved  by  Chambers, 85  35 

ROMAN  CORINTHIAN. 

Example  from  the  Temple  of  Jupiter  Stator, 87  36 

Details  of  the  same, 87  37 

Example  from  the  Pantheon,  at  Rome, 87  38 

COMPOSITE   ORDER. 

Example  from  the  Arch  of  Titus,  at  Rome, 87  39 

Pilasters, 88 

Arcades  and  Arches, 90  40 

Pedestals, 90  41 

Imposts  and  Bases, 92  42 

Balusters  and  Balustrades, 93  43 

GRECIAN  ORDERS. 

Definitions, 94 

Grecian  Doric, 95 

Temple  of  Minerva,  at  Athens, 97  44 


8 


CONTENTS. 


PAGE     PLATE 

Details  of  the  same, i^''  45 

Example  from  the  Temple  of  Theseus,  at  Atliens,. . .  97  46 

Example  from  the  Portico  of  Philip,  King  of  Macedon,  98  47 

Choragic  Monument  of  Thrasyllus, 98  48 

GRECIAN  IONIC. 

Example  from  the  River  Hyssus 99  49 

Details  of  the  same 99  50,  51 

«  u  99  53 

••  ..  100  53 

<c  «  100  54 

Example  from  the  Temple  of  Bacchus, 100  55 

"  "  Miner\-a, 100  55 

Polias  at  Athens 100  50 

Grecian  Architecture, 101 

Choragic  Monument  of  Lysicrates 102  57 

To  draw  Flutes  of  Columns, 102  58 

Bases 102  59 

Entablatures 103 

Designs  for  Cornices, 104  CO,  61 

Chimney-pieces, 104  62,  63 

Doors, 105 

Modern  Doors, 107  64 

Outside  Doors, 107  65 

Ionic  Front  Door, 107  66 

WINDOWS. 

Plan  of  Windows, 110  67 

Design  for  French  Windows, 110  68 

«  Oriel  "  110  69 

Details  of  the  same, 110  70 

Elements  of  Foliage Ill 

To  draw  Ornaments, Ill  71 

Details  from  the  Arch  of  Adrian, 112  72 

Rose  in  the  Arch  of  Titus,  &c., 112  74,  75 

Outline  of  Shaded  Leaf, 112  76 

Composition  of  Foliage, 112  77 

Ornaments  for  Mouldings 112  78 

Ornaments  from  the  Arch  of  Titus, 113  79 

Septimus  Severus, 113  80 

CARPENTIIY. 

Floors, 113 

Partitions 115 


PAGE    PLATK 

Framing, 116 

Trusses, 116    81 

Plan  of  Floor  Framing, 117    82 

Roofs, 117 

Method  of  ascertaining  the  Length  and  Backing  of 

Angle  Rafters, 117    83 

Designs  for  large  Trussed  Roofs, 118    84,  85 

"  Framing  Domes, 118    86 

STAIRS. 

To  find  the  Helinet, 122  87 

Formation  of  the  FaUing  Mould, 122  88 

Scrolls, 125  89,  90 

Application  of  tlie  Mould 126  91 

Resting  Points, 127  92 

Formation  of  the  String, 127  93 

BRIDGES. 

Town's  Bridge 129  94 

Waterloo    "      133  95 

Rural  Villa, 134  96 

Church  Edifice, 134  97 

GOTHIC  ARCHITECTURE. 

DetaUs, 129    98,  101 

Dimensions  of  English  Cathedrals, 139 

BUILDING. 

Mortar, 143 

Masonry,  144 

Stone  Arches 146  102 

Bricldaying, 147 

Plastering, 149 

Mastic  Cement 151 

Lathing  and  Plastering, 153 

Slating, 157 

Plumbing, 160 

Painting, " 166 

Tables    showing  Weight    of   different   Materials, 

Strength  of  Columns,  &c., 1G8 

Glossary  of  Architectural  Terms 171 

Glossary  of  Tcclmical  Terms  used  by  Carpenters 

and  Masons, 178 

Rules  of  Work,  &c., 1 84 


INTHODUCTION. 


The  term  Architecture  is  originally  derived  from 
the  Greek  language,  in  which  it  signifies  the  prin- 
cipal handicraft,  or  mechanical  operation  ;  an  expres- 
sion very  applicable  to  the  construction  of  habita- 
tions for  civilized  men,  without  which  few  of  the 
other  practical  arts  could  be  desirable,  or,  indeed,  of 
any  value  whatever.  La  the  genial  climates  of  the 
interior  of  Asia,  where  human  beings  first  appeared, 
defence  from  the  inclemency  of  the  weather  was 
not  an  object  of  research.  Shelter  from  the  intense 
rays  of  the  sun  and  from  the  torrents  of  rain  pecu- 
liar to  those  climates  ;  protection  from  the  wild  beasts 
of  the  field ;  the  necessity  of  privacy  and  complete 
separation  from  then'  fellow-creatm-es,  —  these  and 
other  motives,  which  might  easily  be  specified,  would, 
nevertheless,  render  architecture,  however  rude  and 
simple,  one  of  the  earliest  arts  of  life.  From  the 
Hebrew  Scriptures,  we  learn  that  it  had  arrived  at 
considerable  perfection,  even  under  the  second  gen- 
eration of  manldnd ;  for  there  we  learn  that  Cain, 
after  the  murder  of  his  brother,  withdrew  from  the 
habitation  of  his  parents,  and  built  a  city  in  a  re- 
mote quarter  of  the  world. 

The  progress  of  architecture  from  rudeness  to 
refinement  is  thus  related  by  Viti'uvius,  whose  cel- 
ebrated treatise  on  architectm-e  appeared  in  Italy  in 
the  reign  of  Augustus  Cfcsar,  about  the  beginning 
of  the  Christian  era.  His  notions  were  formed  on 
tradition  and  conjecture  ;  for  the  vvTitings  of  Moses, 
which  contain  the  most  ancient  account  of  the  origin 
of  the  human  race  and  of  human  society,  were 
either  unknown,  or  generally  disregarded,  in  his  time 
in  Europe. 

"  In  the  fiirst  times,"  says  Vitruvius,  "  men  lived  in 
woods  and  caves  ;  but  at  last,  bon'owing  hints  from 
the  birds,  which  bruit  their  nests  with  equal  ingenu- 
ity and  industry,  they  began  to  form  huts  for  them- 
selves. These  huts  were  probably,  at  first,  conical, 
because  that  figure  is  of  the  most  obvious  construc- 


tion, composed  of  trees  or  branches  fixed  in  a  circle 
on  the  ground,  and  joined  together  in  a  point  at  the 
top  ;  the  whole  covered  with  reeds,  leaves,  and  clay. 
Finding,  however,  in  the  course  of  time,  this  conical 
figure  inconvenient,  on  account  of  the  slope  of  its 
sides,  the  form  of  the  hut  was  changed  to  that  of  a 
cube,  or  of  a  paraUelopiped.  Marking  out  the  space 
to  be  occupied  by  the  intended  structure,  they  fixed 
in  the  ground  upright  trunks  of  trees  to  form  the 
sides,  filling  the  intervals  with  branches,  closely  in- 
terwoven, and  covering  the  whole  with  clay.  The 
sides  being  thus  completed,  four  long  beams  were 
placed  on  the  upright  posts,  which,  being  well  joined 
at  the  angles,  kept  the  sides  firm,  and  likewise  served 
to  support  the  covering  or  roof  of  the  building,  com- 
posed of  other  beams,  on  which  were  laid  beds  of 
reeds,  leaves,  and  clay.  When  the  art  of  construct- 
ing habitations  was  so  far  advanced,  men  bethought 
themselves  of  methods  of  rendering  their 
not  only  commodious  for  present  use,  but 
and  durable.  They  stripped  the  bark  and  other  in' 
equalities  from  the  trunks  and  branches  employed  in 
the  walls,  raised  them  above  the  damp  ground  by 
placing  them  on  flat  stones,  and  covered  each  post 
with  a  flat  stone,  to  throw  oft'  the  rain.  The  spaces 
bettt'cen  the  ends  of  the  joists  were  closed  with  clay, 
and  the  ends  of  the  joists  themselves  were  covered 
with  thin  boards,  cut  in  the  form  of  what  are  called 
triglijphs.  The  position  of  the  roofs  was  also  al- 
tered. Being  flat,  they  were  ill  calculated  for  throw- 
ing off"  the  rain ;  they  were  therefore  raised  up  in 
the  middle,  so  as,  with  the  horizontal  beams  con- 
necting the  uprights  of  the  walls,  to  form  a  triangular 
pediment  or  gable.  From  these  simple  elements, 
architecture  took  its  beginning ;  for  when  wood  was 
found  inconvenient  for  constructing  dm'able  dwell- 
ings, and  men  set  themselves  to  erect  more  solid  and 
extensive  buildings  of  clay  dried  in  the  sun,  or  stone, 
they  still  imitated  the   forms  of  those  parts  which 


dwellings 
elegant 


0.  H.  HrLL  LfBRARY 

Ndf  th  Ciroiina  State  College 


10 


INTRODUCTION. 


necessity  had  originally  introduced.  The  upright 
posts,  with  the  flat  stones  under  and  above  them, 
were  converted  into  columns  with  their  bases  and 
capitals ;  the  beams,  rafters,  and  layers  of  materials 
composing  the  roof  were  gradually  improved  into 
architraves,  friezes,  triglyphs,  cornices,  and  the  other 
ornamental  parts  of  modern  architecture."  So  far 
Vitruvius. 

It  may  be  further  remarked,  that  in  many  coun- 
tries, among  the  rudest  tribes  of  men,  excavations 
and  fissures  of  rocks,  hollows  of  trees,  and  caves  of 
the  earth  have  served  as  habitations.  Travellers  in- 
form us  of  a  tree  growing  in  Africa,  the  hollow  of 
which  affords  a  habitation  for  thirty  negro  families, 
which  is  said  to  be  the  largest  tree  in  the  world. 
They  also  inform  us  of  a  subterraneous  city  or  cave, 
occupied  by  Moors,  in  which  there  are  several  hun- 
dred inhabitants.  Armstrong,  in  his  "Journal  of 
Travels  in  the  seat  of  war  between  Russia  and  Tur- 
key," has  the  following  observations :  "  The  Geor- 
gian or  Tartar  dwellings  are  seldom  to  be  found 
above  ground.  The  tops  are  covered  with  beams  of 
wood,  branches  of  trees,  and,  above  all,  with  a  coat 
of  earth,  which  make  them  level  with  the  ground. 
The  natives  are  frequently  disturbed,  when  sitting 
around  the  fire,  by  the  leg  of  some  unfortunate  cow 
or  camel  making  its  appearance  down  the  chimney ; 
and  it  is  not  uncommon  for  the  lambs  to  fall  through, 
and  spoil  whatever  may  happen  to  be  cooking." 
But  among  a  civilized  people,  the  desire  of  seeking 
for  more  agreeable  habitations  must  be  soon  felt. 
The  nature  of  the  climate  and  the  materials  which  it 
more  readily  afforded  regulated,  in  a  great  degree, 
the  construction  of  the  first  buildings  in  which  men 
sheltered  themselves.  According  to  Diodorus  8icu- 
lus,  the  first  buildings  of  Palestine  were  of  reeds  and 
canes  interwoven,  and  so  compact  as  not  to  admit  of 
the  rain  and  wind.  Wood  appears  to  be  a  material 
so  proper  for  building,  and  so  easily  wrought,  that 
men  would,  in  all  ages,  employ  it  for  these  purposes, 
in  places  where  it  could  be  easily  procured.  The 
branches  of  trees,  stuck  in  the  ground  and  rudely 
interwoven,  formed  a  material  for  constructing  them. 
It  is  probable  that  this  method  of  setting  trees  on 
end,  and  bindhig  them  together  at  the  top  and  bot- 
tom, first  gave  rise  to  the  idea  of  base  and  capital  of 
columns.  When  these  branches  were  daubed  with 
clay,  and  covered  over  with  leaves  and  turf,  they 
presented  a  model  of  those  cabins,  in  which,  accord- 
ing to  Vitruvius,  the  earliest  tribes  of  men  were 
accustomed  to  dwell.  At  first,  before  men  became 
acquainted  witli  edge  tools  of  iron,  trees  were  felled 
by  means  of  fire,  or  by  axes  made  of  -sharp  stones. 
They  undermined  the  trees  by  little  at  a  time,  by 
continuing  a  fire  at  their  roots  ;  and  by  the  same 
means  they  could  divide  a  tree  into  the  requisite 
length.  By  degrees,  however,  tools  for  cutting 
and  smoothing  wood  were  invented.     The  tools  for 


smoothing  were  at  first  nothing  more  than  sharp 
stones,  sufficiently  hard  and  free  from  brittleness. 
Some  of  our  North  American  Indians  make  use  of 
the  same  kind  of  tools  at  the  present  time.  "  The 
use  of  bricks  or  masses  of  clay  formed  in  moulds 
and  dried  in  the  sun,  or  baked  in  stoves,  as  the 
materials  of  buildings,  is  of  very  great  antiquity, 
and  is  a  sufficiently  obvious  invention."  According 
to  Moses,  the  tower  of  Babel  was  built  of  bricks  : 
"  Go  to,  let  us  make  bricks,  and  burn  them  thor- 
oughly :  and  they  had  brick  for  stone,  and  slime  had 
they  for  mortar."  (Gen.  xi.  3.)  Pliny  informs  us, 
that  in  the  most  remote  ages  of  the  Egyptians  they 
made  iise  of  bricks  for  building  their  houses,  and 
tiles  for  covering  them.  To  employ  stones  for  the 
same  purpose  was  very  natiural,  where  they  were 
abundant,  and  found  in  masses  sufficient  to  be 
removed  by  manual  dexterity. 

Ai'chitccture  is  arranged  in  different  orders  and 
styles,  according  to  the  nations  by  whom,  or  the 
country  in  which,  it  was  originally  employed,  such 
as  the  Grecian,  the  Roman,  the  Saxon,  the  Norman, 
the  Saracenic  or  Arabian,  the  Gothic,  (kc.  The 
Grecian  architecture  is  divided  into  the  Doric,  the 
Ionic,  and  the  Corinthian,  so  named  fjom  the  invent- 
ors, or  from  those  parts  of  Greece,  or  of  the  Grecian 
colonies  in  Asia  Minor,  where  each  Idnd  first  ap- 
peared. Roman  or  Italian  architecture  was  divided 
into  the  Tuscan  and  the  Composite  —  the  first  being 
employed,  as  it  is  said,  by  the  ancient  inhabitants  of 
Tuscany,  and  the  last  being  a  later  improvement 
adopted  by  the  Romans,  compounded  of  the  two 
Grecian  orders,  the  Ionic  and  the  Corinthian. 

When  architecture  was  in  its  glory  in  ancient 
Greece,  the  Ionic  was  the  favorite  order,  as  being 
the  most  graceful,  light,  and  elegant.  Of  this  order 
were  the  temple  of  the  Delphic  oracle,  the  temple  of 
Apollo,  at  JNIiletus,  and  the  temple  of  Diana,  at 
Ephesus. 

"  The  Ionic,  then,  with  decent  matron  grace 
Her  airy  pillar  heaved." 

After  the  Ionic,  the  Corinthian  was  introduced, 
in  which  in  attempting  greater  perfection,  they  devi- 
ated from  the  true  simplicity  of  nature.  It  marked 
age  of  luxury  and  magnificence,  when  pomp  and 
splendor  had  become  the  predominant  passion,  but 
had  not  yet  extinguished  the  taste  for  the  sublime 
and  beautiful.  Attempts  were  made  to  unite  all 
these  characters  ;  but  a  corrupted  taste,  only,  was 
pleased,  a  chastened  judgment  was  not  satisfied. 

"  Luxuriant  last, 
The  rich  Corinthian  spreads  her  wanton  wreath." 

In  the  Composite  order,  this  deviation  is  more 
remarkable.  This  was  invented  by  the  Italians; 
and,  although  rich  and  profuse  in  its  ornaments,  dis- 
covers an  obvious  want  of  correct  taste  and  judg- 


INTRODUCTION. 


11 


mcnt,  and  shows  that  the  Grecians  had  cxhausd-d  all 
the  principles  of  grandeur  and  beauty  in  the  original 
orders.  And  in  these  they  had  arrived  at  the  acme 
of  perfection,  because  the  Composite  could  not  pos- 
sibly have  been  introduced  without  combining  all  the 
rest;  conse<iucntly,  that  simplicity  is  desti-oyed,  which 
is  in  conformity  with  nature,  and  the  great  concomi- 
tant of  beauty.  It  is  said  this  order  was  fii-st  used 
by  the  Romans  in  their  ti-iumphal  arches,  to  show 
their  dominion  over  the  people  whom  they  con- 
quered.* 

An  order  in  architecture  consists  of  two  principal 
parts  —  the  column  and  the  entablature,  or  parts 
supported  by  Ihe  column.  Of  these  two  principal 
parts,  each  consists  of  three  subdivisions.  Those  of 
the  column  are  the  base  on  which  it  rests,  the  shaft, 
or  tali  tapering  portion,  and  the  capital,  or  ornament- 
al part  crowning  the  shaft.  Those  of  the  entabla- 
ture are,  first,  the  architrave,  then  the  frieze,  and 
above  all,  the  cornice.  Each  of  the  smaller  parts  is 
again  subdivided  and  distributed  in  various  ways, 
according  to  the  orders  to  which  they  belong,  as  ex- 
isting in  antique  monuments,  but  more  frequently 
according  to  the  taste  and  fancy  of  the  authors  who 
have  ^^^:itten  on  the  subject  of  architecture. 

The  principal  character  of  the  various  kinds  of 
architecture  depending  on  the  column  and  its  requi- 
site accompaniments,  the  whole  is  commonly  and 
almost  universally  divided  into  five  species  or  orders, 
viz.,  the  Tuscan,  the  Doric,  the  Ionic,  the  Corinthian, 


*  An  anonjinous  ■\\Titer  on  the  history  of  architecture  observes, 
that  the  art  is  supposed  to  have  arrived  at  its  glory  in  the  time  of 
Augustus  Ceesar ;  but  was,  as  "vvell  as  other  polite  arts,  neglected 
under  Tiberius.  Nero,  indeed,  notwithstanding  his  vices,  retained 
an  uncommon  passion  for  architecture  ;  but  luxury  and  dissoluteness 
had  a  greater  share  in  it  than  real  magnificence.  In  the  time  of 
Trajan,  Apollodotus  excelled  in  the  art,  by  which  he  obtained  the 
favor  of  that  prince,  and  erected  that  famous  pUIav  called  "  Tra- 
jan's," which  is  remaining  to  this  day.  But  after  this  time  archi- 
tecture began  to  decline,  though  it  was  for  some  time  supported  by 
the  care  and  munificence  of  Alexander  Severus  ;  yet  it  fell  with  the 
western  empire,  and  sunk  into  corruption.  All  the  most  beautiful 
monuments  of  antiquity  were  destroyed  by  the  ravages  of  the  Visi- 
goths, and  from  that  time  architecture  became  so  coarse  and  artless 
that  these  professed  arcliitects  were  totally  ignorant  of  just  design- 
ing, ^^hcrein  the  whole  beauty  of  architecture  consists  ;  hence  a  new 
manner  of  architecture,  called  Gothic,  took  its  rise.  Charlemagne 
industriously  labored  for  the  restoration  of  architecture ;  and  the 
French  applied  themselves  to  it  with  success,  under  the  encourage- 
ment of  Hugh  Capet.  Ilis  son  Robert  prosecuted  the  same  design 
of  modern  architecture,  and,  by  degrees,  ran  into  as  great  an  excess 
of  delicacy  as  the  Goths  had  before  done  of  massivencss.  To  those 
we  may  add  the  Arabesques  and  Moresque  or  Moorish  architecture, 
which  were  much  of  the  same  nature  with  the  Gothic,  except  that 
83  the  former  were  brought  from  the  north  by  the  Goths  and  Van- 
dals, the  latter  was  brought  from  the  south  by  the  Moors  and  Sar- 
acens. The  architects  of  the  thirteenth,  fourteenth,  fifteenth,  and 
sixteenth  centuries,  who  liad  some  knowledge  of  sculpture,  seemed 
to  make  perfection  consist  wholly  in  the  delicacy  and  multitude  of 
ornaments  which  they  lavishly  bc'stowed  on  their' buUdings,  but  fre- 
quently without  conduct  or  taste.  In  the  two  last  centuries,  the 
architects  of  Italy  and  France  assiduously  endeavored  to  retrieve 
the  primitive  simplicity  and  beauty  of  ancient  architecture  ;  nor  did 
they  fail  of  success,  insomuch  that  now  most  churches,  palaces,  &c., 
are  built  entirely  after  the  antique. 


and  the  Comjiosilc.  This  distribution  and  arrange- 
ment would  seem  to  have  been  founded  on  the  pro- 
gressive proportion,  strength,  and  ornament  of  the 
orders ;  they  arc,  however,  well  calculated  to  mislead 
the  student  and  the  architect,  in  tracing  the  origin 
and  gradual  advancement  of  each  order.  Without 
attempting  to  search  for  the  commencement  of  either 
of  the  above  orders,  it  is  sulficient  for  us  to  know 
that  the  Grecians- employed  only  the  Doric,  ihc 
Ionic,  and  the  Corinthian ;  and  that  the  Tuscan  and 
Composite  were  only  used  in  Italy  —  the  one  more 
rude  and  the  other  more  ornamented  than  the  Gre- 
cian orders,  which  occupied  a  middle  rank.  To 
attain,  therefore,  a  proper  knowledge  of  the  princi- 
ples of  architecture,  the  student  ought  to  confine 
himself  to  the  three  Grecian  orders,  not  only  because 
in  them  these  principles  are  most  displayed,  but 
because  of  aU  the  monuments  of  antiquity  which 
have  subsisted  to  modern  times,  few,  perhaps  none, 
can  be  pointed  out  in  Avhich  the  Roman  or  Italic 
mode  of  construction  is  certainly  to  be  traced. 

In  architecture,  various  terms  are  employed  in  a 
peculiar  sense,  of  which  the  following  are  the  chief: 
Column  is  a  Latin  word,  signifying,  in  general,  a 
piUar  or  supporter  of  some  superincumbent  load; 
but  is  now  confined  to  a  round  pUlar,  smaller  above 
than  below,  and  thereby  closely  imitating  the  trunk 
of  a  tree,  from  which  it  was  originally  drawn.  When 
the  pillar  is  not  round  and  tapering,  but  square,  and 
of  equal  dimensions  above  and  below,  it  is  called 
an  ante.  The  column  consists  of  three  principal 
divisions  :  1st,  the  base,  from  the  Latin  term  basis, 
the  foundation  on  which  any  thing  rests  ;  2d,  the 
shaft,  or  circular  tapering  portion  ;  and  3d,  the  cap- 
itaj,  from  the  Latin  term  for  the  head,  or  the  prin- 
cipal member. 

The  base  is  subdivided  into  different  small  parts, 
according  to  the  order  to  which  the  column  belongs ; 
but  all  the  lowermost  part  is  the  plinth,  from  the 
Grecian  term  for  a  brick,  because  the  ancient  bricks 
were  in  general  about  square,  and  comparatively 
thin,  resembling  our  paving  bricks  or  tUes.  Above 
the  plinth  lay  the  torus,  a  round  moulding  resembling 
a  rope,  so  called  in  Greek,  and  imitating  the  band 
tied  round  the  bottom  of  the  original  tree,  as  the 
plinth  did  the  flat  brick  or  stone  on  which  it  stood, 
to  keep  it  fi-om  the  ground.  Between  these  two 
members  was  sometimes  introduced  a  hollow  chan- 
nel, called  scotia,  from  the  Greek  word  for  darkness, 
because  little  light  could  enter  it. 

The  column  was  generally  quite  plain  and  smooth 
in  its  whole  length ;  but  in  buildings  where  ornament 
was  particularly  admitted,  the  shaft  was  cut  into  a 
succession  of  small  perpendicular  channels,  resem- 
bling the  inside  of  a  pipe  or  flute  cut  lengthwise  into 
two  parts  ;  hence  the  shaft  is  cTiWed  fluted.  In  some 
instances,  one  third  part  of  the  flutings  from  the  bot- 
tom was,  as  it  were,  filled  up  with  the   half  of  a 


12 


INTRODUCTION. 


round  rod  lying  in  the  liollow.  It  is  singular,  that 
the  flutings  may  have  been  originally  intended  as 
an  imitation  of  the  natural  hollows  of  the  bark 
of  a  tree,  and  might  therefore  be  expected  in  the 
earliest  productions  of  architecture,  it  is  only  in 
the  more  improved  works  that  fluted  columns  are  to 
be  found. 

The  capital  is  variously  subdivided  and  orna- 
mented in  the  different  orders  —  simple  in  the  Doric, 
more  ornamented  in  the  Ionic,  and  highly  enriched 
in  the  Corinthian.  In  all,  however,  a  narrow  mould- 
ing runs  through  the  shaft,  near  the  upper  end,  called 
the  astragal,  because  it  seemed  to  occupy  the  posi- 
tion of  the  upper  bone  of  the  neck.  Because  the 
word  astragal  also  means,  in  the  Greek,  the  heel,  it 
is,  in  some  treatises  on  architecture,  most  ridiculously 
called  by  that  name.  The  uppermost  member  of 
the  capital  is  the  abacus,  so  called,  as  being  broad 
and  thin,  LLlvc  the  board  or  tablet  employed  by  the 
ancients  in  arithmetical  calculations. 

Tlie  volute  is  an  ornament  introduced  in  the  Ionic 
order,  being,  as  its  Latin  word  implies,  a  spii-al  scroU, 
imitating  the  ends  of  some  flexible  substance  loosely 
rolled  up. 

The  capital  of  the  Corinthian  order  is  encircled  by 
rows  of  leaves  of  difierent  sorts.  The  parts  which 
rest  upon,  and  are  supported  by,  the  columns,  are 
comprehended  under  the  general  name  of  the  entab- 
lature, because,  agreeably  to  the  meaning  of  the  term 
tabula,  in  Latin,  they  consist  of  boards,  planks,  or 
stone  slabs,  of  difierent  forms  and  magnitudes.  The 
entablatm-e  is  a  compound  of  three  principal  parts, 
first  the  architrave,  next  the  frieze,  and,  uppermost, 
the  cornice.  The  architrave  is  so  called,  by  a  name 
partly  Greek  and  partly  Latin,  as  being  the  principal 
beam  which,  resting  on  the  capitals  of  the  columns, 
supports  the  remaining  parts  of  the  entablature.  In 
some  cases  it  is  plain,  in  others  it  is  broken  in  two  or 
three  pieces,  like  so  many  separate  beams  lying  on 
each  other. 

The  frieze  consists  of  one  piece,  but  commonly 
enriched  with  sculptiu-e  of  different  sorts.  In  the 
Doric  order,  this  ornament  consists  of  two  whole 
channels,  and  two  half  channels,  forming  one,  if 
joined  together,  and  therefore  called  by  a  Greek 
name  triglyphs,  or  three  hollows.  The  square  spaces 
between  the  successive  triglyphs  are  called  metopes, 
a  term  expressing  the  hollow  open  spaces  between 
the  beams,  the  ends  of  which  are  represented  by  the 
triglyphs.  In  those  metopes  are  sometimes  repre- 
sented the  head  of  some  divinity,  the  skull  of  some 
animal  used  in  sacrifice,  or  other  emblem  of  the  pur- 
pose to  which  was  destined  the  building  on  which 
the  ornaments  were  introduced. 

The  cornice,  from  the  French  corniche,  and  the 
Latin  corona,  is  so  called  because,  being  the  upper- 
most part  of  1hc  cntablatm-e,  it  croirns  the  whole 
architectm-al  distribution  of  the  columns ;  and  it  is 


divided  and  ornamented  in  different  ways,  according 
to  the  order  employed. 

1.  The  first  Grecian  order  in  point  of  antiquity  is 
the  Doric,  so  named  from  the  Dores,  a  small  tribe  in 
Greece,  or,  as  some  say,  from  Dorus,  an  Aehaian 
chief,  who  first  employed  that  order  in  erecting  a 
temple  to  Juno  at  Aigos.  In  all  the  most  perfect 
specimens  of  this  order  now  remaining,  the  column 
springs  immediately  from  the  foundation,  having  no 
base  properly  so  called,  but  only  a  small  swelling 
round  the  bottom,  resembling  what  we  see  at  the 
root  of  a  tree,  and  sufficient  to  show  that  we  sec  the 
whole  of  the  shaft.  The  base,  we  learn  from  "S^itTU- 
vius,  first  appeared  in  the  Ionic  column.  The  Doric 
column  being  short  in  proportion  to  its  diameter,  and 
consequently  strong,  the  entablature  placed  upon  it, 
is,  of  course,  more  massive  than  tliat  of  the  other 
orders,  being  in  height  one  fourth  part  of  the  total 
height  of  the  column. 

2.  The  Ionic  order  derives  its  name  from  the  Tones, 
a  Greek  people  on  the  east  coast  of  the  Archipelago, 
whose  capital  was  Ephesus,  celebrated  on  many 
accounts,  but  particularly  for  the  magnificent  temple 
of  Diana.  This  admirable  sti'ucture  was  in  length 
425  feet,  and  in  breadth  220  feet.  It  was  surrounded 
on  all  sides  by  a  double  range  of  marble  columns, 
70  feet  in  height,  and  conseqiiently  7  feet  9^  inches 
in  diameter  at  the  bottom. 

The  Ionic  column  is  taller  than  the  Doric,  contain- 
ing 9  diameters,  or  18  modules ;  and,  although  sim- 
ple, is  nevertheless  gi-aceful  and  majestic.  If  the 
Doric  were  meant  to  represent  the  manly,  robust 
figure  of  Hercules,  the  Ionic  might  properly  be  the 
emblem  of  the  dignified  simplicity  and  elegance  of 
Diana.  In  this  order,  as  has  been  already  observed, 
the  base  supporting  the  column  was  first  introduced. 
An  ornament  peculiar  to  the  Ionic  column  is  the 
volute  or  spiral  scroll  already  mentioned,  which  is 
described  by  a  succession  of  portions  of  circles, 
drawn  from  different  central  points.  The  height  of 
the  whole  entablatm-e  is  |  of  that  of  tlie  column, 
being  the  medium  between  that  of  the  Doric,  which 
is  |,  and  that  of  the  Corinthian,  which  is  -j|.  The 
height  of  the  base  is  one  module,  or  half  the  diam- 
eter of  the  shaft. 

3.  The  Corinthian  order  took  its  rise  in  the  flour- 
ishing days  of  Corinth,  a  celebrated  city,  command- 
ing the  communication  of  the  peninsula  of  Pelopon- 
nesus with  the  continent  of  Cireece.  The  beautiful 
foliage  of  the  capital  of  this  order  is  traced  back, 
according  to  Callimachus,  to  the  following  incident : 
A  young  lady  of  Corinth  dying,  her  nurse  carried 
her  playthings  in  a  basket,  the  day  after  her  funeral, 
and  placed  it  on  the  grave.  The  basket,  covered 
with  a  flat  tile,  was  placed  accidentally  on  the  stem 
of  the  plant  acanthus,  which,  sending  out  leaves, 
soon  enclosed  the  basket,  having  their  ends  turned 
downwards  when  they  reached  the  tile.     This  object 


INTRODUCTION. 


13 


struck  the  fancy  of  a  celebrated  sculptor  of  those 
(lays —  Callimachus,  who  immediately  introduced  a 
figure  of  it  on  the  top  of  an  elegant  column  of  his 
invention.  Thus  the  capital  of  the  Corinthian  col- 
umn always  resembles  a  deep  narrow  basket  covered 
with  a  tile,  and  completely  surrounded  by  foliage. 
Such  is  the  account  given  by  Vitruvius ;  but  later 
writers  on  architecture  have  imagined  they  could  dis- 
cover this  ornamented  capital  in  the  description  given 
of  the  temple  erected  by  Solomon,  in  Jerusalem ; 
with  this  difference,  that  there  the  foliage  represented 
branches  of  the  palm,  and  not  the  leaves  of  the 
acanthus.  It  is,  however,  to  be  observed,  that  the 
foliage  of  the  Corinthian  capital  is  frequently  an 
imitation  of  the  leaves,  not  of  the  acanthus,  but  of 
the  olive,  and  of  other  plants,  according  to  the  taste 
of  the  architect.  The  Corinthian  column  is  in  height 
10  diameters,  or  20  modules,  of  which  the  base  is  1 
module  and  the  capital  2^  modules;  consequently, 
the  shaft  measures  16|  modules.  The  entablature 
is  ^  of  the  column. 

1.  The  first  Italic  order  is  called  the  Tuscan,  as 
having  been  employed  by  that  ancient  people,  once 
very  powerful  in  Italy.  It  is,  however,  remarkable 
that  no  vestiges  now  exist  of  any  building  in  which 
the  Tuscan  column  was  employed  to  support  an 
entablature,  or  any  other  weight.  Vitruvius,  it  is 
true,  gives  instructions  for  erecting  temples  accord- 
ing to  this  order ;  biit  it  does  not  appear  that  such 
edifices  were  actually  erected.  The  only  examples 
of  the  use  of  the  Tuscan  column  that  have  come 
down  to  our  times  are  the  admirable  monuments 
still  subsisting  in  their  original  perfection,  the  column 
of  Trajan  and  Antoninus  in  Rome,  and  the  col- 
umn of  Theodosius  in  Constantinople.  The  column 
erected  to  the  honor  of  Trajan,  (next  to  Julius  Cassar 
perhaps  the  most  valuable  of  the  Roman  emperors,) 
who  flourished  a  century  after  Christ,  is,  in  all,  118 
feet  high.  The  shaft  of  the  column  is  in  length 
14i  modules,  or  7i  diameters,  each  11  feet  2  inches. 

The  pedestal  supporting  the  column  is  a  cube  of 
3  modules ;  the  base  is  1  module,  and  the  capital 
I  module.  On  the  capital  is  another  pedestal,  on 
which  stood  a  colossal  statue  of  Trajan ;  but  this 
was  removed,  and  one  of  St.  Peter  now  occupies  the 
same  place.  The  other  column,  commonly  said  to 
have  been  erected  to  Antoninus,  is  of  the  same  Icind, 
but  a  little  smaller.  It  now  supports  the  statue  of 
St.  Paid.  The  magnificent  but  unhappily  situated 
column  or  monument  erected  in  London  to  com- 
memorate the  dreadful  conflagration  which,  in  1666, 
laid  waste  the  greater  part  of  that  city,  although 
copied  from  those  in  Rome,  and  of  considerably 
larger  dimensions,  is  not  properly  Tuscan,  but  a 
fluted  Doric. 

2.  The  other  Italic  order  is  called  the  Composite, 
because  it  seems  to  be  a  combination  of  the  Ionic 
and  the  Corinthian  orders,  to  which  last  it  bears  the 


greatest  resemblance,  imitating  the  former  only  in 
the  adoption  of  the  complete  volute  in  the  capital,  in 
addition  to  the  Corinthian  foliage.  A  specimen  of 
the  Composite  order,  richly  ornamented,  is  to  be  seen 
in  the  triumphal  arch,  of  which  are  represented,  in 
Scripture,  the  golden  candlestick  of  seven  branches, 
and  other  precious  articles  carried  away  from  the  last 
temple  of  Jerusalem. 

Besides  columns,  properly  so  called,  which  are  al- 
ways circular,  another  kind  of  pillar,  caUed  pilasters, 
are  frequently  employed,  especially  where  a  great 
weight  is  to  be  supported.  The  plan  of  a  pilaster  is 
usually  a  square ;  but  those,  the  plan  of  which  is  a 
parallelogram,  are  also  inti'oduced.  The  chief  use 
of  pilasters  is  to  support  arches.  Thus  the  piers  of 
a  bridge  are  in  fact  short  pilasters.  The  arches  sep- 
arating the  nave  from  the  side  aisle  of  St.  Paul  s 
Chm-ch  in  London,  and  of  St.  Peter's  in  Rome,  are 
supported  on  pilasters.  In  some  buildings,  it  is  true, 
we  find  ranges  of  arches  supported  on  columns  of 
even  the  delicate  Corinthian  order ;  but  as  columns 
are  of  a  tapering  form,  the  upper  diameter  being  less 
than  the  lower,  and  as  this  diminution  is  increased 
in  the  eyes  of  the  spectator  by  the  distance  of  the 
upper  part,  the  columns  have  a  slender  and  even  a 
feeble  appearance,  and  consequently  are  ill  adapted 
for  supporting  an  arch.  On  the  other  hand,  pilasters 
being  of  equal  dimensions  all  over  their  height,  and 
very  short  in  proportion  to  then-  diameter,  possess 
a  solidity  and  strength  capable  of  bearing  arches  of 
the  greatest  weight  and  magnitude.  By  pilasters  we 
also  mean  an  ornament  applied  to  walls,  internal  and 
external,  resembling  in  parts  and  form  a  column,  biit 
flattened  instead  of  round.  Pilasters  of  this  sort 
have  their  base,  shaft,  and  capital,  and  are  plain  or 
fluted,  according  to  the  architectural  order  to  which 
they  belong.  It  is  a  matter  still  unsettled  whether 
such  a  pilaster  ought  to  diminish  in  breadth,  like  a 
column,  or  to  retain  the  same  breadth  above  and 
below,  like  a  soM  pier.  Pilasters  usually  project 
one  fourth  part  of  their  breadth  from  the  wall  to 
which  they  are  applied.  Both  columns  and  pilasters 
are  frequently  raised  from  the  gi-ound,  and  on  pedes- 
tals —  a  construction  not  without  its  propriety  in 
certain  cases,  as  in  our  churches,  where  the  galleries 
rest  upon  pilasters,  and  the  front  of  the  gallery  coin- 
cides with  the  pedestal  of  the  column  which  rises  to 
the  roof.  Pedestals  are  by  no  means  essential  to 
columns  or  pilasters  ;  but  when  employed,  they  must 
be  formed  and  ornamented  conformably  to  the  order 
of  the  columns  they  support. 

Columns  are  placed  at  different  distances,  accord- 
ing to  their  destination,  and  the  spaces  between  them 
are  termed  intercolnmniations.  This  separation  in 
the  Greek  orders  varies  firom  one  diameter  and  a  half 
of  the  lower  end  of  the  column  to  four  diameters ; 
but  if  the  Tuscan  column  were  employed,  the  archi- 
trave being  supposed  to  consist  of  beams  of  timber, 


14 


INTRODUCTION. 


the  intercolumniation  may  be  much  wider  than  if  it 
consisted  of  blocks  of  stone.  That  interval,  how- 
ever, between  columns,  which  has  received  the  sanc- 
tion of  the  best  monuments  of  antiquity,  and  of  the 
most  judicious  architects,  is  equal  to  two  diameters 
and  a  quarter  of  the  column.  Hence  it  is  called 
Euslijle,  from  two  Greek  terms  expressing  the  proper 
arrangement  of  columns.  The  latter  term,  stylos,  a 
column,  enters  into  the  composition  of  several  other 
architectiu-al  terms,  as  pycnostyle,  to  express  columns 
placed  close  together  ;  prostyle,  a  number  of  columns 
placed  as  in  a  jjortico  before  the  entrance,  front  of  a 
building,  of  winch  we  have  examples  in  London, 
in  the  Churches  of  St.  Martin-in-the-Fields,  of  St. 
George,  Hanover  Square,  of  St.  George,  Blooms- 
bury,  in  imitation  of  ancient  edifices  in  Rome,  &c. 
When  ranges  of  columns  are  carried  quite  round  the 
outside  of  a  building,  they  form  a  peristyle. 

Ai'ches  may,  perhaps,  be  considered  less  magnificent 
than  ranges  of  columns ;  but  they  are  very  solid,  and 
liable  to  few  accidents.  The  importance  of  arches 
in  afibrding  a  commodious  passage  over  a  river 
needs  no  illustration.  It  has  long  been  the  practice 
to  construct  bridges  of  arches,  increasing  in  width, 
and  consequently  in  height,  from  each  end  to  the 
middle,  so  that  the  road  formed  the  segment  of  a 
large  ckcle.  The  arches  have  also  been  generally 
semicircles.  The  practice  was  first  laid  aside  in 
France,  where  many  noble  bridges  are  now  to  be 
seen,  consisting,  like  the  ancient  Greek  and  Roman, 
of  arches  all  of  the  same  span  or  width,  and  the 
same  height ;  so  that  the  road  is  carried  on  a  level 
all  the  way  along  the  bridge.  In  order  to  keep  the 
bridge  low,  the  arches  vary  greatly  from  a  semicircle, 
being  segments  of  circles  of  large  diameter.  Nay, 
in  some  instances  in  France  the  arches  are  portions 
of  ellipses,  and  not  circular,  by  which  measure  the 
crown  of  the  arch  is  kept  very  low.  On  this  most 
improved  plan  a  bridge  is  eonstrttcted  in  London 
over  the  Thames,  between  Blackfriars'  and  West- 
minster Bridges,  which,  for  excellence  of  materials 
and  structure,  for  magnificent  simplicity  and  extent, 
is  perhaps  without  a  parallel  in  Europe.  It  consists 
indeed  of  only  9  equal  elliptic  arches  ;  but  each  is  of 
120  feet  span.  The  extent  of  each  pier  between  the 
arches  is  20  feet,  and  the  length  of  the  bridge  1280 
feet,  very  nearly  a  quarter  of  a  mile,  on  the  same 
level  line  from  one  end  to  the  other.  To  enable  the 
reader  to  form  some  judgment  of  the  properties  of 
this  work,  (called  the  Strand  Bridge,  because  it  leads 
into  that  street,  on  the  west  side  of  Somerset  Place,) 
the  following  account  of  some  other  remarkable 
bridges  is  given:  Of  the  adjoining  comnumications 
over  the  Thames,  London  Bridge  consists  of  19 
arches,  and  is  in  length  915  feet ;  Blackfriars'  Bridge 
consists  of  9  arches,  and  is  995  feet  long  ;  and  West- 
minster Bridge,  consisting  of  15  arches,  is  in  length 
1223  feet.     The  celebrated  bridge  over  the  Loire  at 


Tours,  in  France,  is  horizontal,  consisting  of  15  ellip- 
tic arches,  and  in  length  1335  feet.  The  bridge  ovei 
the  Moldaw  at  Prague,  the  capital  of  Bohemia,  is  in 
length  1700  feet.  But  these  are  all  far  surpassed  in 
length  by  the  antique  bridge  over  the  rapid  Rhone, 
at  St.  Esprit,  in  the  south  part  of  France,  which, 
constructed  on  a  multitude  of  small  arches,  extends 
to  the  length  of  3000  feet,  possessing  this  singu- 
larity, that,  instead  of  being  straight,  it  consists  of 
two  lines  of  direction,  meeting  in  the  river  at  a  very 
obtuse  angle,  pointed  up  against  the  stream,  as  if  the 
better  to  resist  its  violence. 

In  various  edifices,  ancient  and  modern,  we  find 
columns  and  arches  placed  in  ranges  one  above 
another.  In  such  works  care  must  be  taken  that  the 
more  massive  are  made  to  support  the  more  slender, 
placing  first  the  Doric  order,  next  the  Ionic,  and, 
above  all,  the  Corinthian  or  Composite.  Li  this 
arrangement,  the  upper  diameter  of  the  superior  col- 
umn is  usually  made  equal  to  the  lower  diameter  of 
the  inferior  column,  giving  the  succession  of  columns 
the  an-  of  one  tail,  tapering  tree  cut  into  so  many  sep- 
arate portions. 

The  most  remarkable  edifices  of  antiquity  which 
have  subsisted  with  tolerable  entirencss  to  our  days 
are  temples  of  various  sorts.  The  stntcture  of  these 
temples  is  exti-emely  simple,  the  building  being  a 
parallelogi-am,  seldom  of  great  dimensions.  Some 
have  a  portico  of  columns  at  the  entrance,  and  the 
external  walls  plain  or  adorned  with  pilasters.  Older 
temples,  however,  are  surrounded  on  all  parts  by  a 
single,  and  even  by  a  double,  range  of  columns,  sup- 
porting the  architrave,  frieze,  and  cornice,  together 
with  the  roof;  so  that  the  temple  itself  is  in  a  man- 
ner concealed  from  the  view,  and  receives  no  light 
but  from  the  entrance.  Such  a  construction  is  evi- 
dently very  ill  adapted  to  the  purposes  of  a  Christian, 
and  especially  of  a  Protestant,  place  of  worship.  It 
has  nevertheless  been  imitated  in  many  magnificent 
structures,  Avith  some  alterations  and  the  addition  of 
projections  in  each  of  the  long  sides,  for  the  purpose 
of  resembling  the  cross,  the  emblem  of  the  Christian 
faith.  According  to  the  system  of  divine  service 
which  for  many  centuries  has  prevailed  in  the  Roman 
Catholic  worship,  the  sacred  offices  may  be  con- 
ducted, without  mutual  interference,  in  sundry  parts 
of  the  church  at  the  same  time.  In  the  Protestant 
system,  however,  whether  Lutheran,  Calvinistic,  or 
Anglican,  in  which  nothing  is  done  as  it  were  in 
secret,  and  in  which  every  member  of  the  congrega- 
tion is  to  hear  and  participate  in  every  part  of  the 
service,  sacred  edifices  must,  to  be  useful,  be  iimited 
in  magnitude  and  form.  To  be  satisfied  of  the  truth 
of  this  observation,  it  will  be  qitite  sufficient  to  enter 
St.  Paul's  Church,  in  London,  at  a  time  when  ser- 
vice is  performing.  A  comparatively  small  portion 
of  that  grand  structure  is  set  apart  for  the  congre- 
gation, while    the    great   body  of  the  building   pre- 


INTRODUCTION. 


15 


sents  the  appearance  of  a  vast,  useless  void,  neither 
applied,  nor  indeed  applicable,  to  any  purpose  of  the 
Protestant  worship.  The  same  observation  belongs 
to  the  most  ancient  Gothic  cathedrals ;  but  these 
were  constructed  with  a  very  different  view. 

The  columns  of  the  portico  and  pilasters  of  the 
body  of  St.  Peter's,  at  Rome,  reach  at  once  from  the 
ground  to  the  attic ;  but  in  St.  Paul's,  at  London, 
the  whole  of  the  edifice  is  divided  into  two  ranges 
of  columns  and  pilasters  —  an  arrangement  which, 
by  breaking  the  whole  into  a  repetition  of  small 
parts  and  members,  counteracts  the  etTect  which 
would  be  produced  by  the  great  dimensions  of  the 
edifice  were  it  adorned  with  columns  occupying  the 
whole  height  of  the  building.  On  the  other  hand, 
the  intervals  between  the  grand  columns  of  the  por- 
tico of  St.  Peter's  having  been  built  up  into  two 
stories  of  arcades  and  balconies,  to  accommodate  the 
pope  in  certain  ceremonies,  the  effect  of  the  portico 
is  destroyed  ;  and,  instead  of  one  open  range  of  lofty 
pillars,  the  eye  is  offended  to  see  them  half  sunk,  as 
it  were,  into  a  wall,  the  use  of  which  is  by  no  means 
at  first  sight  apparent.  From  this  material  defect, 
the  front  of  St.  Paul's,  although  broken  into  two 
ranges  of  pUlars,  is  fortunately  free. 

Columns  grouped,  or  placed  tw^o  and  two  together, 
have  always  a  bad  efl'ect ;  for  they  suggest  to  the 
observer  the  idea  that  single  columns  have  been  at 
first  employed,  and,  being  found  too  weak  for  their 
load,  another  set  of  columns  had  been  placed  beside 
them  to  take  off  a  part  of  the  burden.  Grouped  or 
double  columns  are  ^vholly  a  modern  invention, 
nothing  of  the  kind  being  found  in  any  antique 
work ;  and  although  they  were  employed  by  the 
first-rate  architects  who  constructed  the  celebrated 
colonnade  of  the  palace  of  the  Louvre,  in  Paris,  the 
front  portico  of  St.  Paul's,  the  entrance  into  Somer- 
set Place,  in  London,  &c.,  the  grouping  of  columns 
is,  nevertheless,  a  departure  from  the  genuine  rules 
of  the  art. 

Instead  of  different  ranges  of  columns,  it  is  iisual 
to  throw  the  ground  floor  of  an  edifice  into  the  form 
of  a  basement,  on  which  rise  the  columns  or  pilas- 
ters to  ornament  the  front.  This  basement  ought 
never  to  be  less  in  height  than  half  the  length  of  the 
order  it  supports.  Basements  are  generally  rusti- 
cated ;  that  is,  the  stones  are  cut  and  placed  so  as  to 
resemble  the  rude  blocks  as  they  are  supposed  to  rise 
from  the  quarry.  In  the  application  of  this  rusti- 
cation, however,  the  judgment  and  taste  of  the  archi- 
tect wili  be  displayed.  In  London,  we  have  exam- 
ples of  the  judicious  employment  of  rusticated 
walls,  and  of  the  very  reverse.  The  huge,  ponderous 
masses  apparently  in  all  their  native  rudeness  com- 
posing the  exterior  of  Newgate  prison,  admirably 
indicate  and  characterize  the  nature  of  the  edifice. 
The  less  rude,  it  is  true,  but  still  rusticated,  walls  of 
Carlton  House  are,  on  the  contrary,  equally  incon- 


gruous with  tlie  delicate  and  richly-ornamented  por- 
tico, and  with  the  purposes  to  which  that  structure  is 
appropriated. 

When  a  building  is  divided  into  different  floors,  or 
stories,  it  seems  proper  that  each  story  should  have 
its  separate  range  of  columns  or  pUastcrs  which  then 
appear  each  to  support  the  entablature  and  the  pro- 
jecting timbers  of  the  superincumbent  floors.  When, 
on  the  contrary,  two,  and  even  three,  tiers  of  windows 
are  all  included  in  the  height  of  one  range  of  col- 
umns or  pUasters,  the  want  of  use,  and  even  of  con- 
nection, in  columns  of  such  a  length,  must  strUie 
every  observer. 

When  a  range  of  columns,  surmounted  with  their 
proper  entablature,  supports  the  end  of  a  roof,  a  tri- 
angular space  is  formed,  called  the  pediment,  the  two 
incLuied  sides  being  finished  agreeably  to  the  cornice 
below  them,  the  enclosed  ti'iangular  space  or  tympa- 
num is  often  fUled  with  historic  or  emblematic  sciilp- 
ture.  Pediments  on  a  small  scale,  triangular  or  as 
arches  of  circles,  are  frequently  placed  alternately 
over  windows  in  modern  buildings ;  and  instances 
of  the  same  intermixture  are  not  wanting  in  vestiges 
of  ancient  structures.  The  most  proper  proportion 
of  a  pediment,  whether  triangular  or  circular,  is  to 
make  its  perpendicular  height  from  one  fifth  to  one 
fourth  part  of  the  base. 

The  preceding  observations  belong  to  the  Grecian 
and  Roman  systems  of  architecture ;  but  another 
system,  conducted  on  very  different  ideas,  and  of 
which  many  specimens  of  admirable  contrivance  and 
execiition  stiU  adorn  the  principal  states  of  Europe, 
namely,  the  Gothic,  remains  to  be  noticed.  The 
term  is  often  improperly  employed  to  express  every 
mode  of  construction  not  reducible  to  the  ancient 
Grecian.  In  this  way,  works  erected  by  the  Saxons 
and  the  Normans  in  the  northern  and  middle  parts, 
and  by  the  Saracens  or  Moors  from  Africa  in  the 
southern  parts  of  Europe,  are  often  confounded 
under  the  general  name  of  Gothic  with  those  to 
which  that  name  properly  belongs.  This  last  species 
of  building  is  supposed  to  have  first  appeared  in 
England  after  the  conquest,  in  the  reign  of  Henry  II., 
who  died  in  1189 ;  introduced,  most  probably,  fi-om 
Normandy  and  other  parts  of  France,  where  splen- 
did monuments  of  Gothic  architecture  are  very  com- 
mon. 

On  the  origin  of  the  Gothic  mode  of  building,  in- 
genious men  have  varied  much  in  opinion,  and  even 
on  the  origin  of  the  name.  The  Goths  were  in 
early  times  the  inhabitants  of  Sweden;  but  in  the 
decay  of  the  Roman  empire,  they  with  other  north- 
ern tribes  invaded  and  even  overrun  aU  the  southern 
parts  of  Europe,  even  to  the  Straits  of  Gibraltar. 
Ignorant  of  every  art  but  that  of  war,  the  science 
and  skill  introduced  into  those  parts  by  the  Romans 
were  overwhelmed,  and  architecture  gradually  as- 
sumed  forms   unknown    to   the    Romans   and    the 


16 


INTRODUCTION. 


Greeks.  Hence,  buildings  constructed  on  principles 
different  from  those  of  antiquity  came  to  be  dis- 
tingnit^hcd  as  Gothic,  not  because  the  Goths  alone 
were  their  founders,  but  because  the  Goths  and  their 
neighbors  the  Vandals,  having  established  a  regular 
succession  of  kings  in  Spain,  their  name  became 
more  famous  than  that  of  any  other  northern  race. 
The  Saxon,  Norman,  and  Gotliic  styles  of  architec- 
ture, though  nearly  related  in  sundry  particidars, 
have  still  each  its  peculiar  character. 

The  Saxon  and  Norman  agree  in  this,  that  the 
form  of  the  building  is  in  both  the  same.  The  pil- 
lars are  round,  square,  or  polygonal,  and  very  short, 
massive,  and  strong ;  but  the  arches  and  heads  of  the 
doors  and  windows  are  semicircular.  If,  in  these 
particulars,  any  difference  be  found,  it  consists  in  the 
superior  massiveness  and  large  dimensions  of  the 
Norman  architecture.  The  Saxon  churches,  of  which 
sundry  examples,  or  parts  at  least,  have  remained  to 
our  times,  were  often  well  constructed,  and  even 
elegant,  but  generally  of  moderate  size.  Those 
erected  by  the  Normans,  on  the  other  hand,  were 
usually  large  and  magnificent,  can-ied  up  to  a  great 
height,  with  two,  and  even  three,  ranges  of  pillars, 
one  above  the  other,  of  various  dimensions,  but  con- 
nected by  circular  arches.  In  the  centi-e  was  a  lofty 
tower,  with  two  others  at  the  west  end,  where  was 
the  principal  entrance.  In  the  course  of  time,  how- 
ever, the  Normans  introduced  pillars  of  a  much  more 
agreeable  form,  tall  and  slender.  In  England,  the 
Saxon  and  Norman  styles  are  generally  found  mixed 
in  the  same  building  —  the  latter,  introduced  in  the 
twelfth  century,  being  ingrafted  on  the  former,  which 
had  been  in  use  for  centuries  preceding. 

The  principal  marks  by  which  the  true  Gothic 
architecture  is  distinguished  are,  its  projecting  but- 
tresses around  the  exterior  of  the  building,  its  pin- 
nacles and  spii-es,  its  large  branching  windows,  its 
niches,  its  canopies  and  sculptured  angels,  saints, 
and  kings,  the  fretted  roof,  the  clustered  pillar,  but, 
above  all,  the  arch,  always  more  or  less  acutely 
pointed.  As  plainness  and  solidity  constitute  the 
leading  features  of  the  Saxon  and  Norman  build- 
ings, so  the  Gothic  architecture  is  distinguished  by 
the  lightness  of  the  work,  the  lofty  boldness  of  its 
elevation,  the  peculiar  slenderness  of  its  pillars,  the 
profuse  and  delicate  richness  of  its  ornaments,  and, 
we  must  add,  the  astonishing  exceUence  of  the 
masonry. 

In  inquh-ics  into  the  origin  of  the  proper  Gothic 
style  of  building,  we  meet  with  no  less  genius  and 
fancy  than  in  similar  inquiries  concerning  the  Greek 
orders,  and  much  greater  variety  of  sentiment.  Some 
writers  imagine  the  Gothic  style  was  brought  into 
England  Ijy  the  crusaders  on  their  return  irom  the 
Holy  Land  and  other  parts  of  the  East,  and  think 
that  lliis  slylc  should  be  called  Saracenic.  Others 
would  call  it   Moresque,  as   having  been  introduced 


into  Spain  by  the  Moors.  On  the  other  hand,  the 
pointed  arch  which  characterizes  the  Gothic  is,  by 
some,  traced  to  the  intersection  of  two  semicircles, 
svich  as  is  frequently  seen  in  Saxon  buildings  —  the 
one  arch  being  described  from  the  end  of  the  diam- 
eter, and  passing  through  the  centre  of  the  other. 
Such  an  intersection  would  form  an  angle  of  60°, 
and  lines  from  it  to  the  other  extremities  of  the 
arches  would,  of  course,  form  an  eqirilateral  triangle 
—  a  form  certainly  not  unfrcquent  in  Gothic  build- 
ings. The  scheme,  however,  which  has  gained  the 
most  general  assent  is,  that  the  Gothic  is  derived 
from  the  ancient  practice  of  religious  ceremonies 
being  performed  in  groves  of  lofty  trees.  The  eye 
being  accustomed  to  contemplate  the  arches  formed 
by  the  branches  of  trees  that  shaded  their  altars  and 
sheltered  their  assemblies,  it  was  natural,  when  cov- 
ered buildings  succeeded  to  the  groxTJs  as  places  of 
worship,  that  men  should  endeavor  to  introduce  some 
similitude  between  them  and  those  places  in  which 
they  had  been  accustomed  so  long  to  perform  their 
religious  ceremonies.  Accordingly,  we  find  not  only 
the  intersecting  arches  formed  by  the  branches  ex- 
actly imitated  by  the  pointed  arch,  but  also  the  stems 
of  the  trees  as  accurately  represented  by  the  slender 
and  clustering  pillars  of  a  Gothic  cathedral.  Indeed, 
no  attentive  observer  ever  viewed  a  regular  avenue 
of  well-gi-own  trees  intermixing  their  branches  over 
head  but  it  presently  put  him  in  mind  of  the  long 
vista  through  a  Gothic  church,  or  ever  entered  one 
of  the  laro;er  and  more  elesrant  edifices  of  this  kind 
but  it  presented  to  his  imagination  an  avenue  of 
lofty  trees  intermingling  their  branches  over  his  head. 
Under  this  idea  of  so  extraordinary  a  species  of 
architecture,  all  the  irregular  transgressions  of  art,  all 
the  monstrous  offences  against  nature,  as  some  men 
speak,  disappear ;  every  thing  has  its  reason,  every 
thing  is  in  order,  and  an  harmonious  whole  arises 
from  the  studious  application  of  means  proper  and 
proportioned  to  the  end.  For,  could  the  arches  be 
otherwise  than  pointed  where  the  workmen  were  to 
imitate  the  curve  made  by  two  opposite  trees  by 
their  mutual  insertion  into  one  another?  Could  the 
columns  be  otherwise  than  split  into  distinct  shafts, 
when  they  were  to  represent  the  stems  of  a  clump 
of  trees  gi-owing  close  together  ?  On  the  same  prin- 
ciples they  formed  the  spreading  ramifications  of  the 
stonework  in  the  windows  and  the  stained  glass  in  the 
open  interstices,  —  the  one  to  represent  the  branches, 
and  the  other  the  leaves  of  an  opening  grove,  —  both 
concurring  to  preserve  that  gloomy  fight  which,  in 
the  gi-eater  number  of  men,  insph-es  religious  awe 
and  veneration.  Hence  we  see  the  reason  of  theii 
studied  aversion  to  apparent  solidity  in  these  stu- 
pendous masses  of  building,  deemed  so  absurd  by 
men  accustomed  to  the  apparent  as  \vell  as  real 
strength  of  Grecian  architecture  ;  for  the  surprising 
fightness  of  the   Gothic    building,  united  with  real 


INTRODUCTION. 


17 


strength,  was  necessary  to  complete  the  execution  of 
their  original  idea  of  a  sylvan  temple. 

The  origin  of  Gothic  architecture  here  pointed  out 
has  been  very  happily  illustrated  and  exemplified  by 
Sir  James  Hall,  in  a  dissertation  published  in  the 
Transactions  of  the  Royal  Sociely  of  Edinburgh, 
and  in  a  subsequent  separate  publication  on  the  same 
curious  subject,  well  worthy  of  attention. 

In  the  architecture  of  the  Greeks  and  Romans,  the 
columns  were  admired  for  the  elegance  of  their  pro- 
portions ;  but  in  the  Gothic,  the  column  h  seldom,  if 
ever,  diminished  in  diameter ;  nor  do  we  find  any 
fixed  proportion  between  the  diameter  and  the  height 
of  the  column  ;  nor  is  the  intercolumniation  or  space 
between  any  two  pillars  regulated  by  the  diameter  of 
their  height.  Examples  of  the  widest  diflerence  in 
the  intercolumniations  are  common.  For  instance, 
in  the  nave  of  the  Cathedral  of  York,  and  in  the 
aisles  of  the  conventual  Church  of  Newark-upon- 
Trent,  both  edifices  deservedly  admired,  but  widely 
differing  in  the  proportions  of  their  columns  and  the 
intervals  between  them. 

The  Gothic  column  not  being  diminished  above, 
and  having  no  entablature,  is  the  better  suited,  in 
point  of  stability,  to  support  the  arch  springing 
immediately  from  it,  as  only  a  continuation  of  one 
half  of  the  column.  An  arch  sprLngmg  from  a 
Greek  or  Roman  column  has  always,  as  was  before 
observed,  an  unfavorable  effect.  The  striking  im- 
pression of  a  Gothic  structure  is  produced  by  taking 
in  the  whole,  in  all  its  relations ;  but  in  the  Greek 
architecture,  our  pleasure  often  arises  from  contem- 
plating the  elegance  and  fine  proportions  of  its 
several  parts. 

On  viewing  a  Gothic  building,  we  soon  perceive 
how  admirably  the  parts  are  constructed  for  the  eye 
to  embrace  the  whole.  The  column  is  generally  an 
assemblage  of  vertical  mouldings,  or  a  bundle  of 
rods,  enclosing  a  tall  slender  post  or  trunk  of  a  tree 
acting  as  a  conductor  to  the  eye.  The  capitals  pre- 
sent nttle  or  no  interruption  to  the  sight,  which 
glides  up  along  the  pointed  arch,  and  embraces  the 
whole  upper  portion  of  the  edifice.  One  of  the  ver- 
tical rods  forming  the  column  pierces  through  the 
capital,  and  ascends  to  the  roof,  and  firom  it  spring 
the  ribs  of  the  vaulting. 

The  exterior  of  a  Gothic  edifice  has  an  effect  sim- 
ilar to  that  of  the  interior.  The  vertical  rods  of  the 
columns  run  up  to  the  top  of  the  pediment  and  the 
terminating  pinnacle,  and  the  pyramidal  buttresses 
on  the  outside  produce  similar  etfects  on  the  eye  of 
the  beholder. 

GENERAL  OBSERVATIONS  ON  THE   CONSTRUCTION  OF 
HOUSES. 

In  building,  the  situation  is  the  first  point  to  be 
determined.  For  dwellings,  the  position  ought  to  be 
sufficiently    elevated   to    be    free   from   damps    and 

a 


noxious  vapors,  but,  at  the  same  time,  not  ox])oscd 
to  the  wintry  blasts.  The  neighborhood  of  fens, 
marshes,  and  stagnating  waters  should  always  be 
avoided  ;  but  water  for  domestic  uses  should  always 
be  easily  and  plentifully  attainable.  When  a  full 
southern  aspect  cannot  be  procured,  the  next  best  is 
a  western  ;  for  the  heat  is  always  greater  at  ecjual 
distances  from  noon  in  the  afternoon  than  in  the 
morning.  With  respect  to  the  gi-ound  to  be  built 
upon,  it  should  be  carefully  examined  by  boring  or 
sinking  pits.  Stone  or  gravel  afford  the  best  foun- 
dations ;  but  if  these  be  not  of  considerable  thick- 
ness, dependence  ought  not,  in  all  cases,  to  be  placed 
upon  such  soils.  If,  however,  it  becomes  necessary 
to  found  upon  sandy,  or  upon  marshy,  boggy  groiind, 
the  foundation  must  be  secured  by  piling,  planking, 
laying  large  ledges,  or  other  contrivances  of  the  same 
nature. 

The  situation  being  determined  upon,  the  architect 
or  builder  prepares  plans  of  the  intended  edifice,  gen- 
eral and  particular,  with  elevations  of  the  fronts  and 
ends,  not  drawn  as  they  would  appear  to  the  eye  of 
a  spectator,  agreeably  to  the  rules  of  perspective,  but 
according  to  their  general  dimensions  as  measured  on 
a  given  scale.  To  the  plans  of  each  separate  story 
must  be  added  sections  in  length  and  breadth  of  the 
whole  building,  to  show  the  elevation  of  the  internal 
parts.  As,  however,  no  building  can  ever  appear  to 
the  eye  in  the  precise  form  of  a  geometrical  eleva- 
tion upon  paper,  and  as  it  requires  considerable  skill 
and  practice  to  be  able,  from  such  an  elevation,  to 
form  a  judgment  of  the  appearance  of  the  edifice 
when  actually  erected,  it  is  most  satisfactory,  and, 
indeed,  but  just  to  the  proprietor,  to  furnish  him  with 
views  of  the  intended  structure  from  different  points 
of  sight,  accompanied  by  its  attendant  out-buUdings, 
shrubbery,  &c.,  such  as  they  may  be  expected  to  be 
when  brought  to  perfection.  From  the  want  of  such 
general  perspective  representations,  many  a  propri- 
etor has  beheld  with  disgust  or  mortification  the 
completion  of  a  residence  on  which  vast  sums  were 
expended,  and  the  arcliitect  has  very  unjustly  been 
blamed ;  nay,  in  some  cases  ruined  in  his  business,  in 
consequence  of  such  vexations  and  disappointments, 
occasioned  by  his  unscientific  employer.  In  cases  of 
great  public  buildings,  models  of  timber  are  often 
constructed,  which,  when  done  upon  a  properly 
adapted  scale,  convey  a  very  perfect  conception  of 
the  intended  structiures. 

The  external  form,  and  the  internal  distribution  of 
houses,  are  necessarily  susceptible  of  such  variety, 
that  it  is  impossible  to  lay  down  any  particular  rules 
on  these  heads.  A  country  seat  is,  of  late  years, 
usually  arranged  with  a  centre  building  for  the  fam-> 
ily,  and  two  wings,  connected  by  covered  passages 
with  the  centre,  for  various  other  purposes.  The 
proportion  that  these  wings  should  bear  to  the  centre 
has  never  yet   been  ascertained ;  yet  every  passing 


18 


INTRODUCTION. 


spectator  will  exclaim  against  the  architect  when  the 
disproportion  between  the  wings  and  the  cenire 
strikes  him  as  extravagant.  In  some  modern  build- 
ings of  this  nature  we  find  the  length  of  its  wings 
in  front,  each  only  one  third  part  of  that  of  the  cen- 
tre; in  others,  one  half;  but  nothing  has  a  worse 
effect  than  disproportion  between  the  body  and  the 
wings  in  point  of  height.  The  connecting  passage 
or  colonnade  always  looks  best  when  it  forms  exactly 
a  quarter  of  a  circle. 

The  groat  difficulty  in  architecture  is  to  combine 
utility  witli  ornament  and  magnificence.  This  can, 
indeed,  be  properly  done  in  structures  of  a  certain 
extent  alone  ;  but  even  space  and  expense  have  not 
always  been  sufficient  to  insure  these  essential  ends. 

Excess  of  ornament  is  always  misplaced  in  small 
buildings,  which  have  then  more  the  air  of  models 
of  other  great  works  than  real  places  of  abode.  It 
was  observed  of  Chiswick  House,  on  the  banks  of 
the  Thames,  above  London,  (buUt  in  imitation,  but 
on  a  small  scale,  of  a  noted  structure  of  Palladio, 
near  Vicenza,  in  the  north  of  Italy,)  that  it  was  too 
large  to  hang  to  one's  watch  chain,  and  too  small  for 
a  man  to  live  in. 

DOORS. 

The  size  and  proportion  of  doors  must  be  regu- 
lated by  the  purposes  of  the  building  to  which  they 
belong.  The  door  of  a  dwelling-house,  correspond- 
ing to  the  human  size,  is  confined  to  seven  or  eight 
feet  in  height,  and  three  or  four  in  breadth.  In  pri- 
vate hovises,  four  feet  may  be  the  greatest  breadth. 
In  small  doors,  the  breadth  or  width  may  be  to  the 
height  as  three  to  seven  ;  but  in  large  doors,  as  one 
to  two.  Doors  intended  to  have  but  one  leaf,  or 
close,  should  never  exceed  three  feet  six  inches  in 
breadth,  otherwise  the  door  becomes  too  heavy  for 
convenient  use.  Doors  of  a  wider  aperture,  especial- 
ly in  the  outer  wall,  arc  best  formed  with  two  fold- 
ing leaves. 

As  to  the  modern  fashion  of  opening  a  wide  com- 
munication between  rooms  on  the  same  floor,  by 
means  of  broad  folding  doors,  the  practice  sets  all 
rules  of  proportion  completely  at  defiance. 

The  external  lintels  of  doors  and  windows  should 
always  be  on  the  same  level,  and  the  doors  should 
never  be  narrower  than  the  windows.  When  the 
outward  wall  is  ornamented  with  half  columns  and 
arches,  forming  blank  arcades,  the  doors  and  win- 
dows should  just  rise  up  to  the  springing  of  the 
arches. 

The  most  common  way  of  ornamenting  the  aper- 
ture of  a  door  is  by  an  architrave  on  the  top,  and 
also  down  the  sides.  Sometimes  a  cornice  and  even 
a  complete  entablature  may  be  placed  above  the  lin- 
tel. Pilasters  and  semicolumns  have  also  a  good 
effect  when  applied  to  outer  doors.  Porticoes  of  four  or 
more  columns  are  properly  adapted  to  large  buildings. 


WINDOWS. 

The  ininiber  and  size  of  the  windows  of  a  build- 
ing must  be  regulated  by  the  nature  and  purposes  of 
that  building.  The  climate,  the  aspect,  the  extent, 
the  elevation,  even  the  thickness  of  the  walls  must 
be  taken  into  consideration.  When  the  walls  are 
thick,  which  is  commonly  the  case  in  detached  stone 
buildings,  the  windows  may  liave  a  considerable 
opening  inwardly,  which  will  admit  nearly  as  much 
light  as  if  the  whole  aperture  in  the  wall  were  en- 
larged. The  proportions  of  windows  depend  on 
their  situation  ;  only  their  width  ought  to  be  the 
same  in  every  story  —  those  in  each,  however,  being 
proportioned  in  height  to  that  of  the  apartments  in 
each  story.  In  the  principal  floor,  the  height  of  the 
windows  may  be  two  and  one  eighth  to  two  and  one 
thud  of  the  width.  In  the  ground  story,  where  the 
apartments  are  lower,  the  apertures  of  the  windows 
seldom  exceed  a  double  square ;  that  is,  the  height  is 
just  double  the  breadth.  When  the  basement  is  riis- 
ticated,  the  height  is  generally  much  less.  In  the 
second  floor,  the  height  of  the  windows  may  be  from 
one  and  a  half  to  one  and  four  fifths,  or,  rather,  three 
fourths  of  the  width.  The  window  in  the  attics  and 
mezzaninos  or  entresols  may  be  a  perfect  square,  or 
even  lower. 

The  windows  of  the  principal  floor  are  the  most 
enriched.  The  simplest  ornament  of  such  windows 
is  an  architrave  carried  round  the  aperture,  with  a 
frieze  and  cornice  on  the  top.  The  windows  of  the 
ground  floor  are  sometimes  entirely  plain ;  at  other 
times  they  are  surrounded  with  rustics  or  a  regular 
architrave.  Those  of  the  second  floor  are  generally 
closed  with  an  architrave,  crowned  at  times  with  a 
frieze  and  cornice  ;  but  these  last  ornaments  would 
be  improper  in  the  attics.  The  breasts  of  aU  the 
windows  on  the  same  floor  ought  to  be  on  the  same 
level,  and  raised  from  two  feet  six  inches  to  three  feet 
above  the  floor.  In  warm  climates,  or  in  country 
houses  in  our  own  climates,  seated  amid  gardens  and 
pleasure  grounds,  the  windows  of  the  gi'ound  story 
being  cut  dowi:  to  the  floor,  render  the  apartments 
pleasant  and  agreeable.  In  country  houses,  indeed, 
in  France,  Italy,  and  other  warm  parts  of  Europe, 
the  principal  apartments  are  aU  on  the  gi'ound  floor  ; 
and  the  other  floors  diminish  in  height  as  they  rise 
above  it.  The  windows  of  the  ground  floor  being 
cut  down  even  with  the  doors,  .and  thus  affording  a 
ready  communication  with  the  garden  or  lawn,  have 
a  peculiar  propriety.  How  far  the  same  practice  in 
the  windows  of  the  first  and  other  floors,  in  the 
streets  of  large  cities,  by  which  the  damps  and  cold 
of  winter  must  inevitably  penetrate  into  the  apart- 
ments, ought  to  be  avoided,  is  a  point  to  be  decided 
by  those  who  prefer  comfort  and  health  to  absurd- 
ities, however  fashionable. 

Not   contented   with    adopting    usages    suited   to 


INTRODUCTION. 


19 


the  genial  temperature  of  the  south  of  Europe,  a 
stranger  on  passing  along  the  new  quarters  of  Lon- 
don might  be  tempted  to  imagine  himself  transported 
to  the  burning  climates  of  India,  when  he  beholds 
the  fronts  of  the  houses,  whatever  be  their  exposure, 
adorned,  or,  rather,  loaded  and  bloeked  up,  with  vast 
projecting  galleries,  intended,  but  very  unnaturally, 
lo  imitate  the  light,  airy,  and  refreshing  verandas  of 
the  East. 

In  so  far  as  these  galleries  are  on  the  outside  of 
ihe  windows  and  walls,  they  are  certainly  of  use  to 
intercept  the  immediate  action  of  the  sun's  rays. 
On  the  same  account,  what  we  call  Venetian  blinds 
ought  to  be  placed  on  the  outside,  and  not  on  the 
inside,  of  our  windows.  On  the  inside,  they  keep  off 
the  glare  of  the  sun's  rays,  but  not  the  heat,  which 
communicates  to  the  air  of  the  room,  warming  it 
just  as  much  as  if  no  blind  intervened.  On  the  out- 
side, the  blinds  reflect  and  repel  the  heat  as  well  as 
the  light,  and  the  au*  within  the  room  preserves  a 
desirable  coolness  of  temperature. 

The  intervals  of  walls  between  windows  should 
never  be  less  than  the  aperture  of  the  windows,  nor 
in  dwelling-houses  gi-eater  than  twice  that  aperture, 
otherwise  the  light  will  be  deficient.  The  usual  rule 
for  proportioning  the  quantity  of  light  to  a  room  is, 
to  multiply  the  length  of  the  room  by  the  breadth, 
and  the  product  by  the  height.  The  square  root  of 
the  last  product  gives  the  number  of  square  feet  of 
aperture  requisite  for  properly  lighting  the  room. 
Thus,  suppose  a  room  to  be  in  length  32  feet  6 
inches,  in  breadth  24  feet,  and  in  height  15  feet ;  the 
product  of  these  quantities  multiplied  successively 
into  each  other  will  be  1700 ;  the  square  root  of 
which,  in  even  numbers,  — 108,  —  will  be  the  number 
of  square  feet  of  aperture  required  to  lighten  the  room. 
This  quantity,  distributed  among  three  windows, 
gives  36  square  feet  for  each  window ;  the  width  of 
each  being  4  feet,  the  height  must  be  twice  and 
one  fourth,  or  9  feet.  Had  it  been  proper  to  open 
four  windows  in  the  same  room,  each  must  have 
contained  only  27  square  feet ;  and  if  the  breadth  of 
each  were  3  feet  6  inches,  the  height  would  be  7 
feet  8i  inches.  It  is,  however,  to  be  observed,  that 
both  internal  and  external  openings  in  houses,  such 
as  windows,  doors,  &c.,  ought  always  to  consist  of 
the  uneven  numbers,  1,  3,  5,  7,  9,  &c.,  and  never  of 
the  even  numbers,  2,  4,  6,  8,  10,  &c. 

This  rule  cannot  always,  it  is  true,  be  observed  in 
the  confined  spaces  allotted  to  houses  in  towns  ;  but 
in  other  situations,  if  the  number  of  windows  be 
even,  the  door  cannot  be  opened  in  the  centre  of  the 
building,  and  the  want  of  an  equal  corresponding 
extent  and  balance  on  each  side  must  strike  the 
most  careless  spectator.  The  same  rule  is  to  be 
observed  in  distributing  the  arches  of  a  bridge  or 
an  arcade,  the  intercolumniations  of  a  portico  or 
colonnade. 


The  proportions  of  rooms,  in  length,  breadlii,  and 
height,  arc  more  the  objects  of  taste  and  experience 
than  of  geometrical  regulation.  A  circle  or  a  scjuare 
is  a  more  perfect  figure  than  an  oval  or  a  parallel- 
ogram ;  and  a  globe,  a  cylinder,  or  a  cube,  than  a 
parallelopiped.  A  room,  however,  in  the  form  of  a 
cylinder  or  a  cube,  would,  in  general,  be  neither  useful 
nor  agreeable.  The  parallelopiped  is,  therefore,  the 
form  universally  adopted  for  rooms  or  chambers  of 
every  sort,  in  which  the  greatest  dimension  is  the 
length,  the  next  is  the  breadth,  and  the  smallest  is 
the  height.  Some  architects  have  made  the  breadth 
one  half  more  than  the  height,  and  the  length  one 
half  more  than  the  breadth.  Thus,  for  example,  if 
the  height  of  the  room  be  16  feet,  the  breadth  will 
be  24  feet,  and  length  36  feet ;  and  on  the  other 
hand,  if  the  length  be  given,  22  feet  6  inches,  the 
breadth  will  be  two  thirds  of  it,  or  15  feet,  and  the 
height  two  thirds  of  the  breadth,  or  10  feet.  Such  a 
rule,  however,  must  evidently  be  subject  to  many 
modifications. 

The  rooms  on  the  gi-ound  or  the  second  floor  may 
be  of  the  same  length  and  breadth  with  those  on  the 
principal  floor ;  but  if  they  were  of  the  same  height, 
the  impropriety  would  immediately  strike  and  offend 
the  eye.  No  defect  in  proportion,  however,  is  more 
offensive  than  that  in  the  height,  and  none  takes 
more  off  from  the  appearance  of  a  room.  A  low 
apartment,  whatever  be  its  other  dimensions,  never 
can  possess  either  dignity  or  beauty. 

It  is  the  common  remark  of  every  one  who,  for  the 
first  time,  enters  the  matchless  fabric  of  St.  Peter's, 
in  Rome,  that  it  by  no  means  strikes  the  eye  as  so 
vast  as  it  is  known  to  be.  This  effect  arises  from 
the  correct  proportions  of  the  whole  edifice,  in  length, 
breadth,  and  height,  and  of  the  various  members  of 
which  it  consists.  Had  it  been  narrow,  our  attention 
would  have  been  attracted  to  its  great  length.  Had 
the  ceiling  been  low,  we  should  have  been  offended 
by  its  disproportionate  length  and  breadth.  Such, 
on  the  contrary,  is  the  harmony  of  the  several  dimen- 
sions of  the  building,  that  no  excess  or  defect  in 
either  of  them  leads  us  to  institute  a  comparison  be- 
tween them.  It  is  only  by  observing  the  time  neces- 
sary merely  to  walk  round  and  give  a  cursory  glance 
to  the  interior  of  St.  Peter's  that  the  stranger  can  be 
convinced  of  its  prodigious  extent  in  all  directions. 
Comparisons  are  seldom  pleasing,  and  not  always 
just ;  it  would,  therefore,  be  on  many  accounts  unfair 
to  compare  St.  Paul's  of  London  with  St.  Peter's 
of  Rome.  It  must,  however,  be  acknowledged  that 
the  first  view  of  the  former  has  an  effect  very  differ- 
ent from  that  produced  by  the  latter,  the  chief  cause 
of  which  is,  that  the  nave  of  St.  Paul's  is  really 
gloomy,  and  apparently  narrow  and  low  for  its 
length  ;  so  that  the  spacious  and  lofty  dome,  instead 
of  being  only  accessory,  becomes  the  principal  part 
of  the  edifice. 


20 


INTRODUCTION. 


The  proportions  and  dimensions  of  rooms  must  be 
reg^ated  by  their  uses.  A  dining-room  and  a  bed- 
chamber require  very  different  proportions.  A  gal- 
lery for  exercise  in  bad  weather,  especially  if  to  be 
adorned  with  paintings  and  statues,  must  be  of  a 
length  in  proportion  to  its  height  and  breadth,  which 
last  must  be  governed  by  the  necessity  of  possessing 
light  from  windows  on  one  side  only,  to  exhibit  with 
due  advantage  the  paintings  and  sculpture  ranged 
along  the  opposite  side.  A  passage  should  be  just 
wide  enough  to  give  a  convenient  communication 
betw^een  the  several  parts  of  the  house ;  and  if  it  be 
wider,  we  are  offended  with  the  waste  of  space 
which  the  architect  ouglit  to  have  turned  to  some 
other  use. 

There  is  no  part  of  a  building  in  which  the  taste 
of  a  builder  can  be  better  displayed  than  in  the 
position  and  distribution  of  stairs.  Even  in  the 
most  spacious  buildings,  a  step  may  be  made  too 
broad,  so  as  to  require  a  sort  of  effort  to  move  up  or 
down  from  one  to  another.  In  spacious  stairs,  the 
steps  should  vary  from  12  to  18  inches  in  breadth, 
and  from  4  to  7  inches  in  height ;  the  length,  also, 
varies  fjom  6  to  15  feet.  Even  in  small  houses,  a 
step  over  7  or  8  inches  high  would  be  inconvenient ; 
and  the  breadth  should  never  be  less  than  9  inches, 
nor  the  length  shorter  than  three  feet. 

We  have  thus  given  a  pretty  lengthy  account  of 
the  theory  of  Architecture  ;  and  would  now  invite 
the  attention  of  the  student  to  the  subjoined  remarks 
on  the  practical  branch  of  the  science. 

A  competent  knowledge  of  the  methods  of  draw- 
ing on  paper,  and  of  working  in  stone,  timber,  or 
other  materials,  the  several  kinds  or  orders  of  col- 
umns, &c.,  is  absolutely  indispensable  to  enable  the 
architect  to  discharge  his  duty  to  his  employer,  and 
the  artisan  to  execute  his  commission. 

It  has  been  already  mentioned,  that  an  order  of 
architecture  consists  of  three  principal  parts,  viz.,  the 
column,  its  pedestal,  and  its  entablature.  Each  of 
these  parts  is  again  subdivided  into  three  parts,  thus : 
the  pedestal  into  its  base  or  lowest  member;  the 
cubical  body,  called  from  its  figure  the  die  or  trunk  ; 
and  the  cornice  above  all.  The  column  into  the 
base,  the  shaft,  and  the  capital.  The  entablature 
into  the  architrave,  the  frieze,  and  the  cornice. 

To  give  a  minute,  full,  and  perfect  explanation  of 
the  proportions  and  manner  of  constructing  these 
several  members,  with  the  various  ornaments  apper- 
taining to  each,  would  require  an  extent  and  a  num- 
ber of  engravings  totally  incompatible  with  the  de- 
sign of  Ihc  present  work.  Nor  is  this  particular 
explaiialion  deemed  essential;  for  the  number  of 
publications  on  this  head  is  already  so  numerous, 
that  it  is  probable  the  student  will  find  it  more  diffi- 
cult to  determine  which  to  follow  than  to  find  a 
guide.  Our  obser\'ations  will,  therefore,  be  general 
and  limited. 


The  simplest  problem  in  mechanical  architectiu-e 
seems  to  be,  to  determine  the  best  form  for  a  column 
The  length  and  the  weight  (that  is,  the  quantity  of 
materials  in  the  column)  being  given,  it  is  of  impor- 
tance to  investigate  the  form  wliich  affords  the  great- 
est possible  strength  ;  but  it  is  somewhat  difficult  to 
ascertain  the  precise  nature  and  direction  of  all  the 
forces  to  be  resisted  which  act  upon  the  column.  If 
a  column  were  considered  only  as  a  beam  fixed  in 
the  ground,  and  acted  upon  by  a  force  pressing  trans- 
versely, or  on  one  side,  it  ought  to  be  much  tapered, 
and  reduced  almost  to  a  point  at  the  upper  end. 
But  it  is  seldom  that  any  force  of  this  kind  can  be 
so  powerful  as  to  do  more  than  overcome  the  weight 
of  the  column.  The  only  thing,  therefore,  to  be  con- 
sidered, is  the  load  which  presses  on  it  from  above  ; 
hence,  whether  we  regard  the  force  as  tending  to 
bend  the  column  or  to  crush  it,  the  forms  commonly 
employed  appear  sufficiently  eligible.  Some  math- 
ematicians have  erroneously  recommended  the  cyl- 
inder as  the  strongest  form  to  resist  bending  ;  and  in 
this  opinion,  those  who  have  not  considered  the  sub- 
ject are  ready  to  join  them,  because  a  cylinder, 
standing  perpendicularly  on  one  end,  being  of  equal 
thickness,  seems  also  to  be  of  equal  strength  through- 
out. From  the  principles  of  mechanical  philosophy, 
however,  it  can  be  shown  that  the  strongest  form  of 
an  upright  column  approaches,  in  fact,  much  more 
nearly  to  that  of  an  oblong  spheroid  or  spindle  of 
which  the  outside  is  an  arch  of  an  ellipsis.  But  the 
consideration  of  the  flexure  of  a  column  is  of  the 
less  practical  importance  in  architectvure,  that,  ixpon  a 
rough  estimate  of  the  properties  of  the  materials 
usually  employed,  a  column  of  stone  (in  order  to  be 
capable  of  being  bent  by  any  weight  which  will  not 
crush  it)  must  be  at  least  forty  times  as  high  as  it  is 
thick,  although  a  bar  of  wood  or  of  iron  may  be 
bent  by  a  superincumbent  load,  if  its  length  exceed 
about  twelve  times  its  thickness.  But  as,  even  in  the 
Composite  order,  —  the  tallest  and  most  delicate  of 
all,  —  the  height  of  the  column  is  only,  at  the  most, 
ten  times  the  thickness  at  the  base,  the  action  of  the 
incumbent  weight,  in  bending  the  column,  ceases  to 
be  an  object  of  much  consideration.  It  is  only,  then, 
as  a  crushing  force  that  the  weight  requires  to  be 
estimated  ;  and  since  the  lower  parts  of  the  column 
itself  have  not  only  the  weight  above,  but  its  own 
upper  parts,  to  support,  the  thickness  below  ought  to 
be  somewhat  increased.  It  appears,  by  experience 
of  the  direction  in  which  the  fracture  of  a  column  is 
made  when  crushed  by  too  great  a  weight,  that  the 
outline  ought  to  be  made  a  little  convex,  or  to  sweU 
a  little  on  the  outside  of  a  straight  line,  joining  the 
extremities  of  the  shaft,  and  more  curved  above  than 
below.  This  is  the  usual,  but  not  the  universal, 
practice.  An  elliptic  arch  is,  perhaps,  the  most  eli- 
gible outline,  or  a  curve  formed  by  bending  a  rule^ 
fixed    at   the    summit   of    the    column.     It   is   very 


INTRODUCTION. 


21 


natural,  in  forming  a  column,  to  copy  the  working  of 
nature  in  forming  the  trunk  of  a  tree,  which  may  be 
considered,  in  a  general  sense,  as  a  portion  of  a 
tapering  cone,  enclosed  by  straight  lines  joining  the 
top  and  the  bottom.  But,  independent  of  other  con- 
siderations, it  is  to  be  remembered  that  the  great 
load  of  the  boughs,  branches,  and  leaves  act  upon 
the  trunk  of  the  tree  very  differently  from  the  load 
usually  to  be  borne  by  a  column.  A  light-house 
placed  upon  a  rock  in  the  sea  may  be  considered  as 
a  column  erected,  not  to  support  a  weight,  but  to 
withstand  the  action  of  wind  and  water.  If  we  cal- 
culated what  would  be  the  best  form  for  a  wooden 
pillar,  intended  to  remain  always  immersed  to  a  cer- 
tain depth  in  water,  we  should  find  that  a  cone  or  a 
pyramid  would  possess  the  greatest  possible  strength 
for  resisting  the  motion  ,of  water ;  and  a  cone  still 
more  acute  than  this  would  be  equally  capable 
of  resisting  the  force  of  the  wind,  supposing  it  to  be 
less  powerful  than  that  of  the  water.  The  part  be- 
low the  surface  of  the  water  might,  therefore,  be 
widened,  so  as  to  become  a  part  of  a  more  obtuse 
cone,  the  upper  part  remaining  more  slender ;  and 
the  agitation  of  the  sea  being  greatest  at  its  surface, 
the  basis  of  the  pOlar  might  be  a  little  contracted,  so 
as  to  have  the  outline  of  the  lower  part  a  little  con- 
vex outwards,  if  the  depth  of  water  were  consider- 
able. But  in  the  case  of  a  building  of  stone,  the 
strength  often  depends  as  much  on  the  weight  as  on 
the  cohesion  of  the  materials ;  and  the  lateral  adhe- 
sion, which  is  materially  influenced  by  the  weight, 
constitutes  a  very  important  part  of  the  strength. 
For  resisting  a  force  tending  to  overset  the  building, 
the  form  in  which  the  weight  gives  the  greatest 
strength  is  that  of  a  conoid  ;  that  is,  a  solid,  of 
which  the  outline  is  a  parabola,  (a  section  of  a  cone 
parallel  to  its  sides,)  concave  towards  the  axis,  and 
convex  outwardly ;  and  for  procuring,  by  means  of 
the  weight,  a  lateral  adhesion  every  where  propor- 
tional to  the  force,  the  form  must  be  cylindrical. 
Hence,  in  a  building  such  as  this  pillar  is  supposed 
to  be,  no  reasons  appear  why  cither  portion  of  its 
outline,  taken  separately,  should  be  made  convex 
towards  the  axis,  although  the  joining  of  the  two 
cones  might  very  properly  be  rounded  off.  Of  the 
form  adopted  for  a  building  exposed  to  the  violence 
of  both  water  and  wind,  we  have  a  remarkable  ex- 
ample in  the  light-house  erected  on  the  Eddystone 
Rock,  situated  in  the  entrance  of  Plymouth  Haven, 
about  fom-teen  miles  out  from  the  land.  The  top  of 
the  rock  on  which  the  light-house  is  founded  is,  it  is 
true,  constantly  above  the  surface  of  the  water  when 
the  sea  is  calm  ;  but  in  stormy  weather,  every  part 
of  the  building  is  exposed  to  the  action  of  the  waves, 
the  water  being  often  thrown  up  to  a  height  far 
above  that  of  the  light-house  ;  so  that  it  may  be  con- 
sidered as  exposed  to  the  force  of  a  fluid  acting 
more  and  more  forcibly  as  it  is  nearer  to  the  foun- 


dation. On  this  account,  the  architect,  the  late  in- 
genious Mr.  Smeaton,  chose  for  the  walls  a  slope 
concave  outwards,  difl'ering  in  form  but  little  from 
that  which  the  most  accurate  theory  could  have 
pointed  out.  The  building,  however,  is  probably  a 
little  weaker  nearly  as  high  as  the  middle  of  its 
height  than  in  any  other  part.  The  light-house  is 
wholly  composed  of  cut  stone,  and  about  16  feet  in 
diameter  at  the  bottom.  The  height  of  the  building 
is  73  feet  6  inches  from  the  rock  to  the  top  of  the 
cornice ;  thence  to  the  base  of  the  lantern  7  feet  6 
inches  ;  and  thence  to  the  summit  of  the  ball  on  the 
top  17  feet  6  inches ;  making  the  whole  height  98 
feet  6  inches. 

In  diminishing  their  columns,  various  rules  seem 
to  have  been  practised  by  the  ancient  architects. 
Sometimes  the  diminution  began  at  the  base,  the 
shaft  being  formed  by  straight  lines  tending  to  a 
junction  at  a  point  beyond  the  summit  of  the  col- 
umn, by  which  measure  the  shaft  became  a  frustum, 
or  portion  of  a  very  acute  cone.  In  other  instances, 
we  find  the  column  carried  up  perfectly  cylindric,  or 
of  the  same  diameter,  for  one  fourth,  or  more  com- 
monly for  one  third  of  its  height,  at  which  points  the 
diminution  begins,  and  extends  to  the  capital.  This 
junction,  however,  of  the  cylinder  and  the  cone, 
although  the  angle  formed  by  their  outlines  be  al- 
most imperceptible  to  the  eye,  appearing  an  imper- 
fection, it  was  proposed  and  practised  by  eminent 
architects  to  form  the  outline  of  the  shaft,  by  a  curve 
running  within  the  cylinder,  but  without  the  cone, 
from  the  base  to  the  capital,  in  such  a  way  that  the 
diameter  of  the  shaft  was,  in  every  part,  less  than 
that  at  the  base,  but  greater  than  that  at  the  capital. 
The  observations  made  on  this  point  by  Vitruvius, 
the  great  teacher  of  architectural  mechanics,  who 
flourished  about  the  beginning  of  the  Christian  era, 
having  in  late  times  been  misunderstood,  it  is  no 
uncommon  thing,  in  different  parts  of  Eiurope,  (to 
say  nothing  of  our  own  country,)  to  meet  with  col- 
umns, the  outlines  of  which  consist  of  a  curve, 
actually  swelling  outwards,  so  that  at  one  third  of 
their  height  their  diameter  considerably  exceeds  that 
at  the  base  —  a  practice  so  offensive  to  the  eye,  as 
weU  as  to  reason,  as  to  create  wonder  how  it  should 
ever  be  adopted  by  men  who  had  ever  seen,  or  even 
read,  of  the  monuments  remaining  of  ancient  archi- 
tecture. 

The  different  methods  of  giving  to  columns  the 
proper  diminution  and  most  elegant  sweeping  out- 
line are  particularly  described  in  the  body  of  this 
work.  In  this  place,  we  must  content  ourselves  with 
giving  the  following  plain  instructions,  by  which 
every  practical  artisan  may  form  his  model  and  plan 
with  accuracy  sufficient  for  ordinary  occasions  :  — 

Take  the  lower  and  upper  diameter  of  the  shaft 
of  a  column  to  be  drawn.  On  the  centre  of  the 
lower  diameter  describe  a   semicircle,   and  erect  a 


22 


INTRODUCTION. 


perpendicular  to  represent  the  axis  of  a  column. 
Through  the  extremity  of  the  upper  diameter  draw 
a  line  parallel  to  the  axis  of  the  column,  cutting  the 
semicircle  at  the  base.  Now,  divide  the  arc  of  the 
semicircle  made  by  the  intersection  of  the  last-men- 
tioned line  and  the  extremity  of  the  base  line  into 
any  number  of  equal  parts,  the  more  the  better,  as 
into  4,  by  points  marked  1,  2,  3,  &c.  Li  the  same 
way,  divide  the  axis  into  the  same  number  of  equal 
parts,  through  each  of  which  draw  indefinite  right 
lines,  at  right  angles,  to  the  axis.  Through  the 
points  of  the  arc,  at  the  base,  draw  lines  parallel  to 
the  axis,  producing  them  respectively  until  they  meet 
the  transverse  lines  ckawn  through  on  the  axis, 
which  will  thus  become  points  in  the  surface  of  the 
column.  To  assist  in  drawing  these  parallel  perpen- 
diculars, it  will  be  convenient,  through  the  points  in 
the  arc  at  the  base,  to  draw  lines  to  the  axis  parallel 
to  the  diameter,  and  setting  off  a  distance  equal  to 
one  of  these  lines  upon  the  transverse  line  passing 
tlrrough  the  first  line.  Another,  equal  to  that  of  the 
second,  the  points  of  the  axis  will  be  obtained  as 
before.  The  setting  on  the  transverses  through  the 
first  point,  a  distance  equal  to  the  extreme  points : 
in  this  manner,  the  points  on  the  opposite  side  of  the 
axis  may  be  obtained.  K,  now,  nails  or  pegs  be 
fijced  in  the  several  points  in  the  surface  of  the  col- 
umn thus  ascertained,  and  along  them  and  through 
the  two  extreme  points  of  the  upper  and  lower  diam- 
eters a  thin  slip  of  timber,  equally  flexible  in  every 
part,  be  applied,  it  will  show  the  contour  or  section 
of  the  exterior  of  the  column.  The  curve  thus 
formed,  being  carefully  transferred,  will  mark  the 
edge  of  the  rule  to  be  used  in  diminishing  the  shaft. 
In  this  process,  it  is  evident  that  the  more  numerous 
the  points  of  the  surface  ascertained,  the  more  accu- 
rately will  the  slip  of  timber  assume  the  proper  form, 
and  the  diminishing  scale  be  constructed. 

MOULDINGS. 

Although  the  shaft  of  a  column  may  not  admit  of 
any  ornament  on  its  body,  yet,  at  each  end,  in  the 
base  and  the  capital,  various  ornamental  parts  are 
introduced,  in  the  due  disti-ibution  and  proportion  of 
which  consists  their  principal  beauty.  These  arc,  in 
general,  called  mouldings,  because  they  are  always  of 
the  same  shape,  as  if  they  all  proceeded  from  the 
same  mould  or  form.  Mouldings  are,  by  some 
writers,  divided  into  Grecian  and  Roman,  with  a  ref- 
erence to  the  remains  of  the  architecture  of  those 
nations  still  in  existence.  The  difference  consists  in 
this  —  that  the  Romans  generally  employed  circular 
arches  in  their  ornaments,  while  the  Greeks  often 
introduced  parts  of  an  ellipsis,  or  of  some  other  sec- 
tion of  a  cone  varying  from  the  circle.  The  princi- 
ple parts  of  mouldings  are  these :  1st.  The  flat  part 
under  or  above  a  moulding  is  2i  fillet,  as  resembling  a 


bandage  or  turban  tied  round  the  column.  2d.  When 
the  moulding  projects  in  the  form  of  a  quadrant  or  a 
smaller  portion  of  a  circle,  it  becomes  an  echinus 
or  Romano  ovolo,  from  its  likeness  to  a  portion  of 
the  shell  of  a  sea-hedgehog  or  of  a  common  egg. 
3d.  But  if  the  moulding,  reversing  that  figure,  be  a 
hollow  of  the  same  shape,  it  is,  therefore,  called  a 
cave/lo.  4th.  A  small  ])rojecting  semicircular  mould- 
ing is  in  general  called  a  head,  as  particularly  belong- 
ing to  the  astragal,  or  neck ;  but,  5th.  K  the  moulding 
be  much  larger,  with  a  fillet  above  or  below  it,  it 
then  becomes  a  torus,  as  imitating  a  rope  or  cable 
applied  to  the  column.  6th.  If  the  section  be  a  con- 
cave semicircle,  or  scmielLipsis,  it  becomes  a  scotia, 
because  the  interior  is  dark.  7th.  When  the  projec- 
tion is  not  properly  a  part  of  a  circle,  but  rather  of 
an  ellipsis,  or  of  some  other  section  of  a  cone,  re- 
turning in  quickly  at  the  upper  part,  it  is  called  a 
Grecian  ovolo ;  and  the  quick  return  in  it  is  by 
workmen  called  a  quirk.  8th.  A  contour  or  section, 
partly  concave  and  partly  convex,  is  a  ci/matium,  be- 
cause it  imitates  the  waves  of  the  sea.  9th.  If  the 
concave  part  be  uppermost,  it  is  a  ci/ma  recta ;  but 
if  the  convex  part  be  uppermost,  it  is  a  ci/ma  reversa, 
or  ogee. 

VOLUTES. 

A  volute  is  a  kind  of  spiral  scroll,  used  in  the 
Ionic  and  Composite  capitals,  of  which  it  makes  the 
principal  characteristic  and  ornament.  It  has  been 
called  the  ram's  horn,  from  its  figure,  which  bears  a 
near  resemblance  to  it.  Most  architects  suppose  that 
the  ancients  intended  the  volute  to  represent  the  bark 
of  a  tree,  laid  under  the  abacus,  and  twisted  thus  at 
each  extreme,  where  it  is  at  liberty.  Others  regard 
it  as  a  sort  of  pillow  or  bolster  laid  between  the 
abacus  and  echinus,  to  prevent  the  latter  from  being 
broken  by  the  weight  of  the  former  and  the  entabla- 
ture over  it.  Accordingly,  they  call  it  jnthdnus. 
Others,  after  Vih'uvius,  contend  that  it  is  designed  to 
represent  the  curls  or  tresses  of  a  woman's  hair. 

The  number  of  volutes  in  the  Ionic  order  is  four ; 
in  the  Composite,  eight.  There  are  also  eight  angu- 
lar volutes  in  the  Corinthian  capital,  accompanied 
with  eight  other  smaller  ones,  called  helices.  There 
are  several  diversities  practised  in  the  volute.  In 
some  the  list  or  edge,  throughout  all  the  circumvolu- 
tions, is  in  the  same  line  or  plane.  Such  are  the 
antique  Ionic  volutes,  and  those  of  Vignola.  In 
others,  the  spires  or  circumvolutions  fall  back  ;  in 
others,  they  project  or  stand  out.  Again :  in  some, 
the  circumvolutions  are  oval ;  in  others,  the  canal  or 
one  circumvolution  is  detached  from  the  list  of 
another  by  a  vacuity  or  aperture.  In  others,  the  rind 
is  parallel  to  the  abacus,  and  springs  out  from  behind 
the  flowers  of  it.  In  others,  it  seems  to  spring  out 
of  the  vase  from  behind  the  ovum,  and  rises  to  the 
abacus,  as  in  most  of  the  fine  Composite  capitals. 


INTKODUCTION. 


23 


The  volute  is  a  part  of  great  importance  to  the 
beauty  of  the  column  ;  hence  architects  have  invent- 
ed divers  ways  of  delineating  it.  The  principal  are 
that  of  Vitruvius,  which  was  long  lost,  and  at  last 
restored  by  Goldman,  and  that  of  Palladio. 

DRAWING  A  COLUMN. 

In  drawing  a  column  of  any  particular  order,  the 
several  dimensions  and  members  are  measured  by  a 
proportional  scale,  founded  on  the  diameter  of  the 
lower  extremity  of  the  shaft,  immediately  above  the 
projection  of  the  base,  where  the  shaft  becomes  rec- 
tilineal. This  diameter  is  divided  into  t^vo  equal 
parts,  each  being  the  radius  of  the  transverse  section 
of  the  column,  and  it  is  termed  a  module.  The 
whole  diameter  is  subdivided  into  sixty  equal  parts 
or  minutes,  of  which,  consequently,  thirty  are  con- 
tained in  a  module.  These  proportional  quantities 
are  easily  converted  into  real  when  the  lower  diam- 
eter of  the  column  is  given  in  measure.  Thus,  if  the 
lower  diameter  of  a  Doric  column  be  5  feet,  or  60 
inches,  the  module  must  be  2i  feet,  or  30  inches,  and 
each  minute  will  be  1  inch ;  and  the  Doric  column 
being  in  height  8  diameters,  the  height  of  the  given 
column  will  be  40  feet  :  hence  the  entablature,  being 
one  fourth  of  the  height  of  the  column,  its  height  in 
this  case  will  be  10  feet,  and  so  on. 

Li  the  Tuscan  order,  the  height  of  the  column  is  7 
times  the  lower  diameter,  or  14  modules  ;  the  entab- 
lature one  fourth  of  the  column,  and  pedestal  one 
fifth  of  the  height  of  all  the  parts.  Hence,  let  the 
whole  height  of  a  Tuscan  column,  with  its  pedestal 
and  entablature,  be  fLxcd  at  40  feet,  the  pedestal, 
being  one  fifth  of  the  whole,  will  be  8  feet  high. 
The  remaining  32  feet,  divided  by  5,  will  give  nearly 
6  feet  5  inches  for  the  entablature,  and  25  feet  7 
inches  for  the  column,  of  which  the  lower  diameter, 
being  one  seventh,  will  be  nearly  3  feet  8  inches. 
Had  the  order  been  Ionic,  the  whole  height,  40  feet, 
divided  as  before  by  5,  (for,  in  all  the  orders,  the  ped- 
estal is  always  one  fifth  of  the  entire  height,)  would 
have  given  8  feet  for  the  pedestal,  and  the  remaining 
32  feet,  divided  by  6,  would  have  given  5  feet  4 
inches  for  the  entablature,  leaving  25  feet  8  inches 
for  the  column,  of  which  the  ninth  part,  or  2  feet  Hi 
inches,  is  the  lower  diameter.  But,  in  general,  when 
the  whole  height  of  the  column,  with  its  pedestal 
and  entablature,  is  given,  the  several  portions  are 
thus  found  in  all  the  orders.  For  the  Tuscan,  divide 
the  entire  height  by  5 ;  the  quotient  is  the  pedestal, 
and  the  remaining  height,  divided  by  5,  wiU  give  the 
entablature.  The  remainder,  divided  by  7,  gives  the 
lower  diameter  of  the  column.  In  the  Doric,  divide 
the  whole  height  by  5,  for  the  pedestal ;  one  fifth  of 
the  remainder  is  the  entablature,  the  rest  is  the  col- 
umn, of  which  the  eighth  part  is  the  diameter.  Ionic 
—  deducting  from  the  entire  height  one  fifth  for  the 


pedestal,  one  sixth  of  the  remaining  height  is  the 
entablature,  and  one  ninth  of  the  remainder  is  the 
diameter  of  the  column. 


CORINTHIAN. 

After  cutting  off  the  pedestal,  as  before,  the  entab- 
lature is  one  sixth  of  the  remainder,  as  in  the  Ionic ; 
and  one  tenth  of  the  rest  is  the  diameter  of  the  col- 
umn. For  the  Composite  order,  the  same  proportions 
are  employed.  In  laying  down  any  order  on  paper, 
draw  a  perpendicular  right  line  to  represent  the  axis 
of  the  column.  Near  the  bottom,  draw  another  line 
(horizontally)  at  right  angles,  on  which,  from  the 
perpendicular,  set  off  on  each  side  a  distance  equal 
to  a  module,  on  one  half  the  diameter.  On  a  sep- 
arate line  equal  to  this  diameter  form  a  scale  of  sixty 
equal  parts  or  minutes,  by  which  to  measure  all  the 
dimensions,  reducing  them  to  minutes  from  the  num- 
ber of  feet  and  inches  in  which  they  are  usually 
given.  The  construction  of  such  scale  is,  however, 
generally  unnecessary,  from  the  variety  to  be  found 
on  Gunter's  and  other  scales  of  wood,  brass,  &c., 
sold  by  the  makers  of  mathematical  instruments. 
On  the  axis  of  the  column  produced  below  it,  set  off, 
progressively  downwards  from  the  bottom  of  the  col- 
umn, the  heights  of  the  several  members  composing 
the  base  and  pedestal ;  and  through  each  of  those 
points  draw  pencil  lines  at  right  angles  to  the  axis. 
Again  :  from  the  same  bottom  line  of  the  column 
set  up  along  the  axis  the  several  heights  of  the  cap- 
ital, architrave,  frieze,  and  cornice,  drawing,  as  be- 
fore, lines  at  right  angles  through  each  point  thus 
ascertained.  Then,  from  the  axis,  set  off,  on  each 
horizontal  line,  the  proper  projection  of  all  the  sev- 
eral parts  in  order,  by  which  means  the  true  elevation 
and  projection  of  each  \viU  be  obtained.  The  ex- 
tremities of  these  horizontal  lines  are  then  connected 
by  the  fillet,  the  ovolo,  cyma  recta,  &c.,  according  to 
the  kind  of  ornamental  profile  belonging  to  each  par- 
ticular order  of  architecture. 

The  relative  proportions  of  the  various  parts  of 
the  orders  being  accurately  marked  on  the  plates, 
any  account  of  them  here  might  be  regarded  as  a 
work  of  supererogation. 

A  specimen  of  the  Composite  order,  singularly 
rich  and  beautiful,  exists  at  Rome,  in  the  triumphal 
arch  erected  to  commemorate  the  awful  and  pre- 
dicted destruction  brought  upoia  the  city  and  temple 
of  Jerusalem  by  the  Romans,  in  the  year  70,  under 
Titus,   during  the  reign   of  his  father  Vespasian.* 

*  The  remains  of  this  triumphal  arch  stand  very  near  the  south- 
western limits  of  the  ancient  Forum.  They  are  thus  noticed  by 
Theodore  Dwight,  Esq.,  in  the  Journal  of  his  Tour  in  Italy  :  "  It 
(the  arch)  is  built  with  solidity,  of  large  blocks  of  marble,  in  the 
form  of  a  simple  gateway  ;  but  the  deep  channels  worn  into  its  sur- 
face by  time,  and  the  immediate  historical  connection  it  has  with 
the  overthrow  of  Jerusalem,  have  imparted  to  it  a  moral  grandeur 
which   even   superior   antiquity   or   magnitude   alone   could   never 


24 


INTRODUCTION. 


Under  the  arch  are  sculptured  the  golden  candela- 
brum of  seven  branches,  the  tables  of  showbread, 
and  other  spoils  carried  away  from  the  temple.  It  is 
the  ingenious,  and  not  improbable,  fancy  of  some 
eminent  ^^Titers  on  architecture,  that  the  general  idea 
of  the  Composite  order,  as  it  appears  in  the  Arch  of 
Titus,  was  borrowed  by  some  Roman  artist  in  the 
suite  of  that  general  from  the  structure  of  the  Tem- 
ple of  Jerusalem  itself,  after  the  conquest  of  the  city, 
but  before  its  final  overtlirow.  Josephus,  it  is  trvie, 
says  the  columns  of  the  temple  were  Corinthian  ; 
but  the  dilTerences  between  that  order  and  the  Com- 
posite might  not  attract  his  attention,  nor  would 
they  have  been  generally  deserving  of  notice.  At 
any  rate,  the  triumphal  and  tropheal  Arch  of  Titus  is 
the  most  ancient  monument  in  which  the  Composite 
order  is  discovered.  This  arch  possesses  another 
peculiarity,  that  it  is  supposed  to  be  the  first  struc- 
ture of  the  tropheal  or  triumphal  kind  erected  by  the 
Romans  —  an  example  soon  afterwards  imitated  by 
the  abject  adulation  of  the  people,  or,  rather,  by 
the  insulting  vanity  of  their  princes,  until  at  last 
such  trophies,  being  lavished  without  discrimination, 
ceased  to  be  marks  of  honorable  distinction. 

The  feelings  and  duties  of  human  beings  in  a 
social  state  of  existence  natiurally  spring  from  that 
state.  To  a  person  brought  up  from  infancy  in  abso- 
lute solitude,  such  feelings  would  only  produce  mis- 
ery, and  such  duties  would  be  a  nonentity.  Let, 
however,  two  persons  be  placed  in  mutual  commu- 
nication, and  that  instant  feelings  of  kindness  or 
dislike,  of  affection  or  hatred,  will  arise.  Let  both 
be  hungry,  and  let  an  apple  or  an  orange  only  be 
procured ;  this  each  will  instinctively  desire  to  appro- 
priate to  himself,  for  an  equal  distribution  of  the 
object  of  their  desires  between  them    must  be  the 


possess.  Those  who  have  read  the  Scriptures  &om  infancy,  and  been 
taught  to  mourn  with  the  saints  and  prophets  of  Israel  over  the  des- 
olation of  the  city  of  David  and  the  house  of  God,  can  never  ap- 
proach, unaffected,  and  regard  this  monument  of  heathen  triumph. 
As  we  entered  the  shelter  of  the  arch  we  trod  the  stones  of  the 
old  Sacred  Way,  which  lay  yet  undisturbed  under  our  feet  —  prob- 
ably the  same  pavement  that  Titus  passed  over  in  his  triimiphal 
march  to  the  Capitol,  when  they  brought  the  spoils  of  the  Holy 
Temple  and  a  largo  company  of  Jewish  captives.  On  the  right  are 
seen,  beautifully  sculptured  in  relief,  the  seven  golden  candlesticks, 
the  silver  trumpet,  the  table  of  showbread,  and  the  book  of  the  law, 
all  borne  by  priests  marching  in  order  ;  and  on  the  other  side  is  the 
emperor  in  his  triumphal  car,  drawn  by  four  horses  harnessed 
abreast,  and  represented  with  the  highest  skill  of  the  sculptor.  The 
chariot  is  accompanied  by  the  Genius  of  the  Senate  and  Victory, 
bearing  a  crown  of  a  branch  of  palm  from  Palestine.  This  record 
of  history,  containing  more  details  than  I  have  enumerated,  still 
speaks  to  the  eye  and  to  the  mind  in  language  as  clear  and  impres- 
sive as  when  it  was  first  erected.  But  the  unyielding  spirit  of  the 
captives  retains,  to  tliis  day,  all  its  pride  .ind  sternness.  There  are 
many  Jews  now  in  Home,  the  descendants  of  the  prisoners  of  Titus ; 
but  it  is  said  that  not  a  son  of  Israel  has  ever  passed  this  detested 
Bpot,  and  trodden  this  part  of  tlic  Sacred  Way,  since  the  day  of  his 
triumph.  They  still  delight  to  trace  back  their  pedigree  to  those 
whose  humiliation  they  have  inherited  ;  while,  it  is  said,  not  a  man 
in  being  can  establish  a  clear  and  undoubted  claim  to  the  blood  of 
any  ancient  Roman  family." 


result  of  posterior  experience  and  reflection,  and  not 
the  spontaneous  suggestion  of  the  occasion.  If  the 
one  is  a  little  stronger  or  more  alert  than  the  other, 
he  w'\\\  avail  himself  of  these  advantages  over  his 
fellow-being  to  seize  the  object  of  his  wishes.  By 
this  sole  appropriation,  the  other  sustains  not  an 
imaginary,  but  a  real,  loss.  The  natural  desire  for 
necessary  aliment  will  aggravate  his  feelings  of  dis- 
appointment and  defeat  into  aversion,  resentment, 
and  revenge  against  his  spoiler ;  and  should  lie  be 
frequently  thwarted  in  a  similar  way  by  his  com- 
panion, notliing  short  of  the  entire  destruction  of 
that  companion  will  appear  sufficient  to  secure  him- 
self from  future  privations  and  sufferings.  This 
process  will  take  place  in  the  breast  of  the  weaker 
being,  even  although  the  stronger  should  not  attempt 
to  assitme  to  himself  still  greater  advantages,  in 
consequence  of  his  acknowledged  superiority.  That 
the  latter  will,  however,  be  governed  by  sentiments 
so  moderate,  is  extremely  improbable.  Tlie  self- 
gratulation  arising  from  consciousness  of  power 
wiU  yield  a  flower  too  delicious  not  to  induce  the 
desire  of  again  experiencing  such  delight.  He  will 
thus  naturally  be  disposed  to  exercise  his  superior 
faculties,  not  when  the  calls  of  necessity  only,  but 
when  the  suggestions  of  vanity  or  caprice,  may  fiu-- 
nish  opportunity.  Hence,  his  feebler  neighbor  will, 
by  degrees,  be  reduced  to  absolute  slavery,  depend- 
ent on  the  other  for  even  the  necessary  means  of 
existence ;  and  of  this  existence  itself,  should  he 
long  continue  refractory,  he  will  probably  be  at  last 
deprived.  Thus  may  be  traced  the  origin  of  the 
worst  feelings  and  actions  by  which  human  beings 
are  distinguished ;  and  by  a  similar,  bttt  opposite, 
process,  may  the  rise  and  progress  of  the  best  senti- 
ments and  conduct  be  explained.  In  absolute  se- 
questration and  solitude,  neither  virtue  nor  vice  can 
exist ;  but  without  virtue  and  vice  in  society,  human 
beings  can  have  no  existence.  When  this  simple 
and  obvious  theory  of  what  is  called  the  origin  of 
evil  (a  theory  by  far  too  simple  and  too  obvious  to 
have  fixed  the  attention  of  presumptuous  philosophy 
in  any  period  of  the  world)  is  considered,  it  will  ex- 
cite no  surprise  that  the  history  of  mankind,  imder 
even  the  most  favorable  circumstances,  sliould  pre- 
sent little  else  than  an  endless  chain  of  deplorable 
wickedness  and  WTctchedness,  equally  the  natural 
consequences  of  folly  and  vice.  "  We  are  a  con- 
temptible gang  of  plunderers,  pests  of  society,  mer- 
iting, forsooth,  punishment  the  most  severe  and  dis- 
graceful, because  we  appropriate  to  ourselves  the 
property  of  unoffending  men,  and  even,  on  some 
occasions,  deprive  the  owners  of  life ;  and  all  this  we 
do,  few  in  number,  more  frequently  by  secret  strat- 
agem than  by  open  force,  and  even  in  some  measure 
authorized  by  the  sanction  of  necessity.  Thou,  on 
the  other  hand,  born  to  independence,  to  wealth,  to 
power,  to  supreme  dominion,  without  even  a  rival  to 


INTRODUCTION. 


25 


attempt  to  obstruct  the  gratification  of  thy  desires, 
without  provocation,  without  invitation,  without  ne- 
cessity, without  any  motive  or  reason  which  a  man 
of  genuine  coru'age  and  truth,  a  friend  to  human  kind, 
would  avow ;  thou  destroyest  cities,  the  abode  of  in- 
dustry, knowledge,  and  patriotism  ;  thou  layest  waste 
peaceable  and  flourishing  countries,  where  thou  hast 
received  no  injury ;  thou  causest  to  flow  torrents  of 
the  blood  of  nations  who  never  even  heard  of  thy 
name ;  and  all  this  thou  dost  at  the  head  of  armed 
myriads,  in  open  defiance  of  common  justice  and  hu- 
manity ;  therefore  art  thou  exalted  to  the  rank  of  a 
hero,  a  conqueror  of  worlds,  a  demigod."  In  such  a 
strain,  we  are  told,  was  the  mighty  Alexander  of 
Macedon  addressed  by  the  chief  of  a  petty  band  of 
pirates  who  fell  into  his  hands,  and  whom  he  con- 
ceived himself  autliorized  to  punish,  in  an  exemplary 
manner,  for  their  outrages  on  society ;  and  the  obser- 
vations are  fully  warranted  by  the  undeviating  prac- 
tice of  aU  people  and  of  aU  times.  Hence,  we  find 
in  the  most  ancient  records  of  human  society  ap- 
plause and  reward  lavishly  bestowed  on  the  successful 
warrior,  whether  just  or  unjust  the  cause  in  which 
he  was  engaged.  But,  beside  tliis  and  other  marks 
of  the  real  or  supposed  admiration  and  gratitude  of 
their  armies  and  people,  conquerors  were  in  the  habit 
of  constructmg  some  more  substantial  evidence  of 
their  victories  on  the  scene  of  their  exploits. 

At  one  time  a  rude  block  of  stone,  at  another  a 
mould  or  liillock  of  stones  and  earth,  raised  on  the 
field  of  battle,  served  at  once  to  point  out  the  spots 
where  the  honors  of  the  victor  were  achieved,  and 
where  rested  from  their  toils  the  human  beings  thus 
cut  off  in  the  performance  of  the  duties  he  imposed. 
Of  such  monuments  many  examples  still  survive  the 
long  lapse  of  ages,  in  Great  Britain  —  in  Cornwall,  in 
Wales,  and  in  Scotland.  These  dumb  memorials 
came  at  last  into  disrepute  ;  they  recorded,  indeed,  a 
slaughter  and  a  victory ;  but  succeeding  generations, 
when  tradition  grew  feeble  or  entirely  died  away, 
were  left  to  conjecture  the  cause  of  their  erection ; 
and  the  mighty  warrior  was  thus  bereft  of  half  his 
glory.  When  the  Romans  began  to  establish  them- 
selves in  the  southern  parts  of  Gaul,  and  to  extend 
the  boundaries  of  their  province,  now  Provence,  Lan- 
guedoc  and  Dauphiny,  in  France,  they  first  constructed 
durable  memorials  of  the  success  usually  accompany- 
ing the  exertions  of  united  and  well-disciplined  bands, 
although  far  firom  numerous,  against  countless  mul- 
titudes of  irregular,  ungovernable  barbarians.  Two 
Roman  generals,  Domitius  ^nobarbus  and  Fabius 
Maximus,  erected  on  the  banks  of  the  Rhone,  saxosw 
turres,  towers  built  of  stone,  supporting  trophies,  con- 
sisting of  arms  offensive  and  defensive,  standards, 
instruments  of  martial  music,  and  other  pledges  of 
victory  taken  from  the  ancient  CJauls.  This  conduct 
on  the  part  of  their  commanders  was  highly  reproved 
at  Rome ;  for  untQ  then  the  Romans  had  never  al- 

4 


lowed  themselves,  even  after  their  most  signal  success 
in  war,  to  erect,  in  the  midst  of  a  conquered  people, 
any  monument  whatever,  by  which  they  should  be 
reminded  of  their  subjection,  and,  consequently,  be  ex- 
cited to  endeavor  to  regain  their  former  independence. 
"  Never  before  this,"  says  the  historian,  "did  the  Ro- 
man people  upbraid  any  conquered  nation  with  their 
own  defeat."  This  happened  about  one  hundred  and 
twenty  years  before  England's  era.  Some  time  after- 
wards, Pompey  constructed,  on  the  summit  of  the 
Pyrenees,  near  their  eastern  extremity,  a  permanent 
building,  as  a  memorial  of  his  successes,  slight  enough, 
indeed,  over  the  partial  but  patriotic  attempt  of  the 
Spaniards  to  throw  off"  the  Romish  yoke.  This  ac- 
tion was  severely  reprobated  at  Rome.  The  same 
magnanimous  sentiment  actuated  not  the  free  states 
of  Greece  only,  but  even  the  despotic  and  military 
kingdom  of  Macedon.  "  States  and  nations,"  said 
those  ancients,  "like  individuals  and  families,  will 
differ  upon  particidar  points,  where  their  interests,  real 
or  supposed,  are  concerned.  These  differences  will 
lead  to  quan-els,  and  even  to  the  most  hostile  proceed- 
ings and  opeir  warfare.  It  is  not  unnatural  that,  in 
these  contests  in  arms,  the  victors  should  endeavor  to 
confirm  the  courage  and  ardor  of  their  own  people, 
and  to  depress  the  spirit  of  their  adversaries,  by  some 
public  testimony  of  their  superiority.  For  such  a  pur- 
pose, a  few  helmets,  and  breastplates,  and  shields, 
and  swords,  taken  from  the  vanquished  and  supported 
against  a  spear,  or  suspended  on  a  tree,  on  the  scene 
of  victory,  will  be  fidly  sufficient :  let  not,  however, 
such  emblems  of  superiority  be  of  long  duration. 
The  passions  of  men  will  cool,  their  views  of  interest 
will  change,  and  the  parties  which  to-day  meet  with 
deadly  rancor  in  the  field  will  be  found  in  a  short 
time  united  in  one  common  cause,  and  fighting,  as 
friends  and  brothers,  against  an  ally  of  one  of  the 
parties  on  a  former  occasion,  but  now  become  a  com- 
mon foe.  It  is,  besides,  to  be  considered  that  suc- 
cess in  war  is  not  always  attached  to  one  side ;  no 
nation  was  ever  always  victorious,  nor  always  dis- 
comfited. Let  us  never,  therefore,  by  permanent  rec- 
ords of  our  temporary  superiority,  labor  to  cherish  and 
foment  among  oiur  neighbors  that  spirit  of  hostility 
which,  at  no  distant  day,  it  may  be  equally  our  de- 
sire and  our  interest  entirely  to  extinguish.  Lijuries 
men  often  will,  and  do,  forgive ;  insults,  perhaps, 
never."  Such  were  the  wise  and  magnanimous  sen- 
timents and  principles  of  the  Greeks  and  Romans,  the 
two  most  enlightened  nations  of  antiquity,  in  their 
best  days.  In  the  degenerate  days  of  Titus  and  Ves- 
pasian, however,  when  Rome  reigned  paramount  over 
the  greater  portion  of  the  civilized  world,  the  feeling 
of  national  importance  and  independence,  the  source 
and  support  of  every  manly,  generous,  and  patriotic 
principle,  was  next  to  extmct  in  the  nations  of  Eu- 
rope. The  example  set  in  the  case  of  Titus  was 
speedily  followed ;    and  not   only  Rome   itself,  but 


D.  H.  HILL  LfBRARY 
North  Carolina  Stafe  College 


26 


INTRODUCTION. 


numbers  of  tlie  principal  cities  over  the  empire,  were 
adorned  with  edifices,  triumphal,  tropheal,  and  com- 
memoratory,  many  of  which  stiU  remain,  exhil)iting 
admirable  specimens  of  architecture  and  sculj)ture, 
and,  by  the  inscriptions  and  representations  with  which 
they  are  charged,  serving  to  illustrate  and  establish 
the  dates  of  laiany  important  historical  facts.  Wis- 
dom, justice,  and  moderation  arc  immutable ;  and, 
as  such,  never  (let  weak,  and  consequently  narrow- 
minded,  men  say  what  they  may)  can  be  inexpedient 
or  out  of  season.  Human  nature  is,  at  this  day,  what 
it  was  twenty  centuries  ago.  Let,  then,  the  prudence 
and  humanity  by  which  states  were  then  governed, 
and  not  the  overbearing  presumption  and  insolence 
on  the  one  hand,  and  tlie  abject,  interested  adulation 
on  the  other,  by  which  later  periods  have  often  been 
characterized,  suggest  the  most  commendable  models 
for  modern  imitation. 

But  to  return  to  the  jVixh  of  Titus.  It  may  be  just 
to  add,  that  the  unfortunate  branches  of  the  Hebrew 
nation  established  in  Rome  made  an  arrangement, 
many  years  ago,  with  the  government,  agi-eeably  to 
which,  for  the  payment  of  a  certain  sura  of  money, 
they  were  permitted  to  open  a  naiTow  passage  by  the 
side  of  that  arch,  which,  although  not  now  connected 
with  the  inhabited  part  of  the  town,  is  situated  in  the 
heart  of  the  old  city,  on  a  very  public  thoroughfare, 
that  then-  minds  might  not  be  tortured  unnecessarily 
by  the  display  of  the  emblems  of  the  final  dcsti-uction 
and  extinction  of  their  religion  and  their  state,  of 
their  name  and  their  nation.  This  digression  the 
reader  will,  it  is  trusted,  without  difficulty  pardon. 
It  arose  natm-ally  from  the  subject,  and  may,  per- 
haps, suggest  certain  considerations  not  entncly  un- 
profitable. 

With  respect  to  the  kind  and  degree  of  ornaments 
to  be  introduced  into  a  column  and  its  appendages, 
it  is  a  maxim,  founded  in  our  natural  sentiment  of 
what  is  decorous  and  beautiful,  that  if  we  are  in 
doubt  concerning  the  proper  medium,  we  should  al- 
ways stop  short  of  the  proposed  point,  and  be  careful 
never  to  go  beyond  it.  The  pupU  of  an  ancient 
painter  in  Greece  produced  a  Venus  loaded  with  jew- 
els. "  Unable  to  make  the  goddess  bcautifid,"  said 
his  master,  "  you  have  thought  to  atone  for  that  de- 
fect, by  making  her  rich  and  fine."  The  dignified 
sobriety  and  gravity  becoming  an  edifice  appropriat- 
ed to  religious  purposes  or  to  the  senatorial  and 
legislative  assemblies  of  a  great  and  enlightened  peo- 
ple; the  massive  solidity  and  strength  inherent  in  our 
idea  of  a  forh'css;  the  light,  airy,  exhilarating  notion 
attached  to  the  name  of  a  theatre  or  other  places  of 
amusement,  —  all  these  qualifications  of  the  edifices  to 
be  conslrneted  will,  to  an  architect  of  genius,  suggest 
the  species  and  (he  measure  of  the  ornament  suitable 
to  each.  A  slender,  delicate,  and  highly-enriched 
Corinthian  portico  to  Newgate  prison  could  not  be 
more  incongruous,  nor  indicate  a  greater  want  of 


taste  in  the  builder,  than  a  massive,  heavy,  clumsy 
Doric  (if  Doric  it  be)  range  of  pUlars,  and  their  pedi- 
ments coiTcspontUng  —  apparently  forbidding,  but 
doubtless  meaning  to  invite,  the  passing  sh-anger  to 
enter  the  theatre  of  Covcnt  Garden.  When  we  ex- 
amine the  monuments  remaining  from  antiquity,  we 
find  that  the  cyma,  the  cavetto,  or  other  ornament, 
formed  by  cutting  into  the  substance  of  the  work, 
is  employed  as  a  finishing  only,  and  never  where 
strength  is  required ;  that  the  ovolo  and  talon  are 
employed  to  support  the  essential  parts  of  the  entab- 
lature, such  as  the  modillions,  dentils,  and  corona ; 
that  the  principal  use  of  the  torus  and  astiagal  is  to 
secm-e  and  strengthen  the  extremities  of  the  columns, 
being  also  employed  for  the  same  purpose  in  pedes- 
tals, carved  so  as  to  resemble  a  rope  or  cable,  agree- 
ably to  the  original  signification  of  the  term  torus ; 
that  the  scotia  serves  merely  to  separate  the  members 
of  the  base,  as  does  also  the  fillet,  not  only  in  the 
base,  but  in  profiles  of  all  kinds.  By  the  term  pro- 
file, is  here  meant  the  assemblage  of  parts,  mouldings, 
and  ornaments  of  a  cornice,  &c.,  in  which  the  eleva- 
tion and  projection  of  each  member  are  exhibited. 
The  most  perfect  profiles  are  those  consisting  of  the 
fewest  mouldings,  adapted  to  the  order  of  the  column, 
so  disposed  that  the  right  lined  and  the  cm-vcd  mem- 
bers succeed  one  another  alternately.  In  every  profile 
one  member  should  be  predominant,  to  which  all  oth- 
ers must  appear  subordinate  :  thus,  in  a  cornice,  the 
corona  is  the  chief  member,  the  cyma  of  the  cavetto 
covers  and  defends  it  from  the  rain,  while  the  modil- 
lions, dentils,  ovolo,  and  talon  serve  to  support  it. 
In  the  arrangement  of  the  exterior  of  a  building, 
whatever  does  not  tend  to  characterize  its  destina- 
tion, however  beautiful  in  itself,  is  always  misplaced. 
Greatness  of  character  in  an  edifice  is  principally 
produced  by  largeness  and  simplicity  of  parts ;  such 
parts,  not  only  by  their  own  magnitude,  but  by  the  gi-eat 
masses  of  light  and  shade  tliey  exhibit  when  fully 
illuminated,  excite  the  idea  of  grandeur.  An  object 
may  be  gi'cat,  and  not  be  grand  ;  but  gi-andeur  and 
smallness  of  parts  are  incompatible.  One  of  the  most 
extensive  edifices  in  Europe  is  the  King  of  Spain's 
palace,  at  the  Escurial,  not  far  from  Madrid.  It 
covers  a  vast  extent  of  gi'ound,  enclosing  a  number 
of  courts,  porticoes,  chapels,  &c.,  in  its  bosom.  Hav- 
ing, however,  been  constructed  as  a  monastery  rather 
than  as  a  palace,  (for  the  royal  apartments  are  con- 
fined to  a  very  small  portion  of  the  structure,  the 
building  is  divided  into  various  floors,  and  conse- 
quently, the  exterior  walls  are  pierced  with  various 
ranges  of  comparatively  small  windows,  adapted  to 
the  cells  and  halls  of  monks.  The  consequence  of 
all  this  is,  that  the  idea  of  grandeur  and  magnificence 
raised  in  the  mind  of  the  spectator,  while  approach- 
ing it  from  a  distance  and  observing  its  prodigious 
dimensions,  entirely  vanishes  away,  when,  on  a  closer 
view,  the  whole  is  discovered  to  be  only  an  assemblage 


INTRODUCTION. 


27 


of  small  diminutive  parts  and  members,  such  as 
might  be  suitably  introduced  into  a  manufactory,  a 
barrack,  a  hospital,  or  a  convent.  Many  objections 
have  been  made  to  Blenheim  Palace,  in  Oxfordshu'e, 
England,  as  clumsy,  ponderous,  inelegant,  and  by  no 
means  corresponding  to  the  customary  notion  of  a 
country  residence.  That  magnificent  edifice  was 
erected,  at  the  expense  of  the  nation,  to  commemo- 
rate the  signal  victory  obtained  in  1704,  near  Blen- 
heim, a  village  on  the  north  bank  of  the  Danube,  by 
tlie  allied  army,  under  the  Duke  of  Marlborough. 
That  distinguished  and  modest  commander  stands, 
next  to  Julius  Ctesar,  unrivalled  in  history  for  perfect 
coolness  and  possession  of  himself  in  action ;  who, 
so  far  from  ever  exposing  himself  to  the  possibility 
of  being  svu-priscd,  whatever  might  have  been  the 
talents  of  his  opponent,  never  rested  until  he  was  so 
close  upon  the  enemy  as,  in  many  cases,  to  discover 
their  measures,  and  prevent  their  forming  any  project 
against  himself  for  the  greater  part  of  the  campaign. 
Like  Cirsar,  also,  in  person  a  hero,  he  was  scrupu- 
lously tender  of  the  lives  of  his  men,  and,  to  spare 
them,  would  often  forego  the  opportunity  of  a  bril- 
liant, but  sanguinary  and  i;seless  victory,  for  the  more 
slow,  but  more  secure  and  difficult  advantages  to  be 
obtained  by  a  sldlful  occupation  of  ground.  On  a 
due  consideration  of  the  destination  of  Blenheim,  it 
will  be  manifest  that  the  architect,  Sir  John  Vanburg, 
intended,  by  throwing  the  structure  into  a  variety  of 
large,  projecting,  and  retmng  masses  of  building,  to 
produce  broad  and  powerful  eflccts  of  light  and 
shade,  and  by  that  contrivance  to  fill  the  spectator 
with  the  idea  of  the  vast  magnitude  of  the  parts  and 
of  the  whole  far  beyond  what  their  real  magnitude, 
considered  as  it  is,  could  be  expected  to  excite. 

Besides  regular  columns  and  pilasters,  we  some- 
times meet,  in  ancient  and  modern  architecture,  en- 
tablatiu'cs  supported  by  human  figures.  These  are 
termed  Cari/atidcs,  from  the  following  circumstance  : 
Five  hundred  years  before  our  era,  Xerxes,  the  power- 
ful monarch  of  Persia,  led  a  prodigious  army  and 
fleet  against  the  free  and  independent  republics  of 
Greece.  Successful  at  first,  more  by  treachery  than 
by  valor,  he  was  at  last  discomfited  at  every  point, 
and  compelled  to  return  in  disgrace  and  ruin  to  his 
own  country.  Carya,  a  town  of  Peloponnesus,  had 
basely  formed  a  league  with  the  invader ;  and  upon 
his  flight  it  was  besieged  by  the  other  states,  levelled 
to  the  ground,  the  male  inhabitants  put  to  the  sword, 
and  the  unhappy,  perhaps  innocent,  females  reduced 
to  slavery  of  the  severest  land.  To  perpetuate  to 
future  ages  the  infamy  and  punishment  of  the  people 
of  Carya,  in  Athens,  and  in  many  other  parts  of 
Greece,  buildings  were  erected,  in  which  were  intro- 
duced, in  the  place  of  columns  and  pilasters,  figures 
of  Caryan  women  supporting  the  load  of  a  cornice 
and  entablature.  In  general,  these  figiu-es  are  at- 
tached, like  pilasters,  to  the  wall ;  but  in  Athens  they 


arc  also  found  detached,  and  performing  the  duty  of 
columns.  Male  figures  are  also  employed  in  the 
same  way  in  some  ancient  buildings  in  Greece  and 
in  Rome  ;  in  Greece,  they  are  evidently  intended  to 
represent  Persian  prisoners  taken  from  Xerxes. 
From  this  account,  it  is  evident  that  human  figures, 
in  the  place  of  columns  or  pilasters,  ought,  if  at  all, 
to  be  introduced  on  very  particular  occasions  indeed. 
They  nevertheless  are  often  seen  in  the  palaces  of 
princes,  and  even  in  private  dweUmgs.  Our  churches 
themselves,  in  which  all  adventitious  distinctions 
among  mankind  ought,  if  any  where,  to  disappear, 
are  not  free  from  this  absurdity.  These  poor  females, 
humiliated,  borne  down  with  a  heavy  load,  are  meant, 
we  are  to  understand,  for  the  Muses  and  the  Graces, 
the  Vu-tues,  and  the  Angels  themselves.  Could  the 
vices  which  corrupt,  and  the  furies  which  torment,  the 
human  race  be  thus  chained  down,  and  so  rendered 
in  some  sort  subservient  to  our  use,  such  an  applica- 
tion of  Persians  and  Caryatides  might  easily  be 
reconciled  to  reason. 

Not  only  entire  human  figures,  but  simple  busts, 
are  also  employed,  occasionally,  to  support  the  entab- 
latiues  of  monuments,  chimney  pieces,  &c.  The 
head  is  placed  on  a  stand,  smaller  below  than  above ; 
and  the  whole  is  called  a  term,  from  terminus,  a 
boundary,  the  Roman  name  of  the  landmarks  or 
march  stones  erected  on  fields  and  possessions  to 
point  out  the  boundaries  between  the  lands  of  differ- 
ent proprietors.  The  protecting  charge  of  these  land- 
marks, as  of  every  thing  else  connected  with  the  affaks 
of  industry  and  commerce,  being  intrusted  to  Mer- 
cury, by  the  Romans  as  well  as  the  Greeks,  the  top 
of  the  stone  or  post  was  carved  in  resemblance  of  his 
head ;  so  that  to  destroy,  or  remove,  or  deface  such 
monuments  was  regarded  not  only  as  gross  uijustice 
to  men,  but  as  a  voluntary  and  impiovis  offence 
against  the  powers  above. 

It  now  remains  to  give  a  few  observations  on  the 
constructions  of  bridges,  one  of  the  most  important 
and  difficult  applications  of  architectural  skill. 


CONSTRUCTION  OF   EraDGES. 

By  a  bridge,  we  mean  a  structure  of  stone,  brick, 
timber,  or  iron,  erected  over  a  river,  a  canal,  a  vaUey, 
or  other  depression  in  the  ground  ;  and  supported  on 
piers  and  arches,  or  on  posts,  for  opening  a  communi- 
cation for  passengers,  cattle,  and  carriages  across 
from  the  one  side  to  the  other. 

The  perfection  of  a  bridge  consists  in  its  having  a 
good  foundation,  that  it  may  be  dm-able  ;  of  an  easy 
ascent  and  descent,  that  it  may  be  convenient ;  and 
of  a  just  proportion  in  its  several  parts,  that  it  may 
be  beautiful.  Bridges  should  always  be  placed  at 
right  angles  to  the  course  of  the  river,  &:c.,  and  the 
piers  should  never  be  thicker  than  is  just  necessary 


28 


INTRODUCTION. 


to  support  the  structure  against  the  force  of  the 
current. 

The  simplest  theory  of  the  arch  supporting  itself 
in  eqiiilihrio  (that  is,  in  such  a  state  that  the  ten- 
dency of  every  part  to  fall  down  or  give  way  is  per- 
fectly equal)  is  that  of  Dr.  Hookc,  the  greatest  of  all 
philosophical  mechanics,  who  flourished  in  tiie  latter 
part  of  the  seventeenth  century.  The  arch,  when  it 
has  only  its  own  weight  to  bear,  may  be  considered 
as  the  reverse  of  a  chain  suspended  freely  at  each 
end ;  for  the  chain  hangs  in  such  a  form  that  the 
weight  in  each  link  is  held  in  equilibrio  by  the  result 
of  the  tsvo  forces  acting  at  its  extremities.  Two 
forces,  or  tensions,  are  produced,  the  one  by  the  weight 
of  the  portion  of  the  chain  below  any  particular  link, 
the  other  by  the  same  weight,  increased  by  that  of 
the  link,  both  of  them  acting  originally  in  a  vertical 
direction.  Now,  supposing  the  chain  inverted  so  as 
to  constitute  an  arch  of  the  same  form  and  weight, 
the  relative  situation  of  all  the  lines  indicating  the 
direction  of  the  forces  will  remain  the  same,  the 
forces  acting  only  in  contrary  directions  ;  so  that  they 
are  compounded  in  a  similar  manner,  and  balance 
each  other  on  the  same  conditions,  but  with  this  dif- 
ference, that  the  equilibrium  of  the  chain  is  stable, 
and  that  of  the  arch  is  tottering.  When  the  links  are 
supposed  to  be  infinitely  small,  and  the  curvatiu-e  of 
the  chain  is  greatest  in  the  middle,  the  chain  forms 
what  is  called  a  catenarian  curve,  from  catena,  a  chain. 
In  common  cases,  this  form  of  an  arch  differs  but 
little  from  a  circular  arch  of  about  one  hundred  and 
twenty  degrees,  or  one  third  of  a  whole  cncle,  rising 
ftom  the  abutments,  with  an  inclination  of  thirty 
degrees  to  the  perpendicular ;  the  arch,  however,  be- 
comes more  curved  at  some  distance  below  the  sum- 
mit, and  then  again  less  curved.  The  supposition, 
however,  of  an  arch  resisting  a  weight  acting  only  in 
a  vertical  dhection,  is  by  no  means  perfectly  applica- 
ble to  cases  usually  occurring  in  practice.  The  pres- 
sure of  loose  stones  and  earth,  moistened  as  they  gen- 
erally must  be  by  rain,  is  exerted  very  nearly  in  the 
same  manner  as  the  pressure  of  fluids,  which  act 
equally  in  all  directions;  and  even  if  the  stones  and 
earth  were  united  in  a  solid  mass,  they  would  consti- 
tute a  sort  of  wedge,  and  produce  a  pressure  of  a 
similar  nature. 

A  bridge  must  also  be  so  calculated  as  to  support 
itself  without  being  in  danger  of  fallmg  by  the  de- 
fect of  the  lateral  adhesion  of  its  parts.  Li  order 
that  it  may,  in  this  respect,  be  of  equal  strength 
throughout,  the  depth  at  each  point  must  be  propor- 
tional to  the  weight  of  the  parts  beyond  it.  This 
property  belongs  to  the  logarithmic  curve  alone,  the 
length  being  made  to  correspond  with  the  logarithm 
of  the  depth.  But,  in  the  construction  of  bridges,  it 
is  necessary  to  inquire  what  is  the  best  form  for  sup- 
porting any  weight  which  may  occasionally  be  placed 
on  the   bridge ;   in   particular,  on    its  weakest  part. 


which  is  usually  the  middle  of  the  arch.  Supposing 
the  depth  at  the  summit  of  the  arch  and  at  tiie  abut- 
ments to  be  given,  it  may  be  considerably  reduced  in 
the  intermediate  parts,  without  impairing  the  strength; 
and  whether  the  road  along  the  bridge  be  horizontal 
or  a  little  inclined,  it  is  agreed  that  an  elliptic  arch, 
not  differing  much  from  a  circular,  is  the  best  calcu- 
lated for  complying,  as  much  as  possible,  with  all 
necessary  conditions. 

The  tier  of  bricks  cut  obliquely,  which  is  placed 
over  a  door  or  window,  is  a  real  arch,  but  so  flat  as 
to  allow  the  outline  to  appear  horizontal.  Little 
dependence,  however,  can  be  placed  on  so  flat  an 
arch,  since  it  j^roduces  a  lateral  thrust,  that  might 
easily  overpower  the  resistance  of  a  side  wall.  For 
the  horizontal  force  required  to  support  each  end  of 
an  arch  is  always  equal  to  the  weight  of  a  quantity 
of  the  materials  supported  by  its  summit,  supposed 
to  be  continued  of  their  actual  depth,  to  the  length 
of  the  radius  of  the  circle,  of  which  the  summit  of 
the  arch  is  a  portion.  This  simple  calculation  will 
enable  an  architect  to  avoid  such  accidents  as  but  too 
often  happen  to  bridges  for  want  of  sufficient  firm- 
ness in  the  abutments.  Very  eminent  modern  arclu- 
tects  have  sometimes  been  less  successful  in  con- 
structing arches  of  bridges  and  other  edifices  than 
those  of  former  times,  whom  it  is  but  too  common  to 
despise ;  and,  for  want  of  attention  to  mechanical 
principles,  they  have  committed  such  errors  in  their 
attempts  to  procure  an  equilibrium  as  have  been 
followed  by  the  most  mischievous  consequences. 
Examples  of  this  mismanagement  might  be  pointed 
out  in  the  bridges  of  our  own  country,  and  the 
churches  of  others ;  but  if  we  are  masters  of  the  true 
nature  and  action  of  pressure,  we  shall  be  able  to 
avoid  similar  errors,  unless  some  defect  in  the  mate- 
rials, the  foundation,  &c.,  occur,  Avhich  could  not  be 
foreseen. 

It  is  desirable  that  the  piers  of  bridges  should  be 
so  firm  as  to  be  able  not  only  to  support  the  weight 
of  half  of  each  adjoining  arch,  but  always  to  sustain 
the  side  thrust  of  one  of  them,  should  the  other  give 
way.  The  same  condition  is  necessary  for  the  sta- 
bility of  walls  of  any  kind  employed  in  supporting 
an  arched  or  vaulted  roof;  hence  the  utility  of  the 
external  buttresses,  which  strengthen  and  adorn 
Gothic  structures.  There  are  two  w^ays  in  which  a 
pier  or  a  wall  may  give  way ;  it  may  either  be  over- 
set, or  caused  to  slide  away  horizontally.  But  since 
the  friction  or  adhesion  ■which  resists  the  side  motion 
is  usually  greater  than  one  third  of  the  pressure,  it 
seldom  happens  that  the  whole  thrust  of  the  arch  is 
so  oblique  as  not  to  produce  a  sufficient  vertical 
pressure  for  secm'ing  the  stability  in  this  respect', 
and  it  is  only  necessary  to  make  the  pier  heavy 
enough  to  resist  the  force  which  tends  to  overset  it 
It  is  not,  however,  the  weight  of  the  pier  only,  but 
that  of  half  of  the  arch  which  rests  on  it,  that  resists 


INTRODUCTION. 


29 


every  effort  to  overset  it ;  and,  in  order  that  the  pier 
may  stand,  the  sum  of  these  weights  acting  on  the 
end  of  a  lever,  equal  to  half  the  thickness  of  the  pier, 
must  be  more  than  equivalent  to  tlic  horizontal 
thrust  acting  on  the  whole  height  of  the  pier.  The 
pier  may  also  be  considered  simply  as  forming  a 
continuation  of  the  arch ;  and  the  stability  will  be 
preserved  as  long  as  the  curve  indicating  the  direc- 
tion of  the  pressure  remains  within  its  substance. 
The  dimensions  of  the  piers  must  depend  on  the 
size  and  form  of  the  arch,  as  also  on  the  force  of  the 
current  to  be  opposed.  In  tide  rivers,  the  current 
acts  twice  a  day  in  contrary  directions,  rising  consid- 
erably above  the  surface  of  the  river  itself,  and  re- 
turning to  that  level.  The  pressure  on  the  piers  is, 
therefore,  very  unequal ;  and,  from  the  circumstance 
that  the  stones  must  be  thus  in  a  continual  alteration 
between  wet  and  dry,  the  selection  and  placing  of 
the  materials  becomes  a  matter  of  the  greatest  im- 
portance. Some  persons  are  of  opinion  that  blocks 
of  stone  resist  the  action  of  water  and  sun,  of 
wet  and  dry  weather,  best,  when  placed  exactly  in 
the  same  position  as  when  they  lay  in  the  quarry. 
Whether  this  circumstance,  if  real,  was  attended  to 
or  not  in  the  construction  of  Blackfriar's  Bridge,  in 
London,  or  whether  the  stone  was  of  an  improper 
kind,  it  is  certain  that  such  parts  of  the  piers  as  are 
exposed  to  be  covered  by  the  tide  are  now  in  a  state 
of  manifest  decay,  while  the  corresponding  parts  of 
Westminster  Bridge  are  comparatively  but  little 
affected,  although  it  was  founded  in  1738,  and  the 
former  bridge  not  till  1760.  The  new  Strand  Bridge 
is  built  of  granite,  the  least  svibject  to  decay  of  all 
stone  from  external  causes.  The  stone  employed  in 
constructing  the  grand  quay  along  the  front  of  the 
arsenal  of  Woolwich,  in  England,  was  drawn  from 
the  vicinity  of  Dundee,  in  Scotland,  and  is  found  to 
answer  much  better  in  such  a  situation,  where  it  is 
alternately,  with  short  intervals,  wet  and  dry,  than 
any  formerly  employed.  It  has  been  likewise  used 
in  some  of  the  great  basins  and  docks  in  London, 
and  in  constructing  the  piers  to  support  the  iron 
bridge  over  the  Thames,  at  Vauxhall. 

In  building  a  bridge,  the  most  essential  part  of 
the  enterprise  is  to  secure  a  good  foundation.  The 
most  simple  method  of  doing  this,  and  carrying  up 
the  piers  to  the  ordinary  height  of  the  water,  is  to 
turn  the  river  out  of  its  course,  above  the  position  of 
the  bridge,  into  a  new  channel  opened  for  it,  near 
the  place  where  it  makes  an  elbow  or  bend,  or  by 
raising  an  enclosure  round  the  spot  where  the  pier  is 
to  be  buUt,  to  keep  out  the  water,  by  driving  a  double 
row  of  piles  into  the  bed  of  the  river,  very  near  one 
another,  with  their  tops  above  the  siurface  of  the 
water.  Hurdles  are  then  put  within  this  double 
row  of  piles,  the  side  of  the  row  which  is  next  the 
intended  pier  is  closed  up,  and  the  hollow  between 
the   rows   filled   with   rushes   and   mud,    so    closely 


rammed  down  that  water  will  not  pass  through. 
The  mud,  sand,  stones,  &c.,  within  this  enclosure, 
are  dug  out,  until  a  solid  foundation  appears.  When 
such  a  foundation  cannot  be  found,  one  of  wooden 
piles,  having  their  lower  ends  well  charred  to  prevent 
rotting,  and  driven  into  the  bottom  of  the  river  as 
close  together  as  possible,  must  be  made.  Some 
architects  have  formed  a  continued  foundation  the 
whole  length  of  the  bridge,  and  not  merely  under  the 
piers.  In  doing  this,  first  one  part  of  the  river  is 
excluded,  and  then  another,  until  the  whole  foun- 
dation be  laid.  When  a  river  is  but  of  moderate 
depth,  having  such  a  bed  as  may  serve  for  a  natural 
foundation,  capable  of  bearing,  without  subsidence, 
in  whole  or  in  part,  a  heavy  pier,  then  a  strong  frame 
of  oak  is  constructed,  and  kept  upon  the  surface  by 
boats  around  it.  On  this  frame  is  laid  a  thick  stra- 
tum or  layer  of  stone,  cramped  together  by  iron  bars, 
and  united  by  strong  terras  mortar,  the  whole  of 
which,  being  then  specifically  heavier  than  the  water, 
is  suffered  gently  to  sink  down  to  the  bottom,  where 
the  pier  is  to  stand.  If  it  be  required  to  construct  a 
bridge  across  a  fordable  river,  or  a  canal,  where  the 
covu'se  of  the  water  may  be  turned  off,  either  by  a 
wooden  fence  placed  obliquely  across  the  river  or  by 
a  channel  dug  one  side,  then  a  dam  must  be  formed 
entirely  across  the  stream,  with  pUes  at  a  convenient 
distance  above  the  place  of  the  intended  bridge. 
The  ground  is  then  dug  out,  until  a  proper  solid 
foundation  presents  itself,  and  all  the  piers  may  be 
founded  and  raised  up  to  the  usual  height  of  the 
river  at  the  same  time ;  after  which,  the  river  is  per- 
mitted to  return  to  its  original  channel.  When  the 
stream  is  by  far  too  considerable  to  be  tiu-ned  aside, 
coffer  dams  are  formed,  of  a  circular  shape,  to  enclose 
the  spot  where  each  pier  is  to  be  built.  The  dam  is 
made,  as  before  said,  by  driving  into  the  bed  of  the 
river  a  double  row  of  stout  piles,  either  charred  at 
the  lower  end,  when  the  bed  is  easily  penetrable,  or 
shod  for  several  feet  with  ii'on  where  it  is  hard.  The 
pUes  are  forced  into  the  ground  by  repeated  blows 
from  the  pile  engine ;  the  piles  are  covered  with 
boarding,  without  and  within,  so  as  to  be  tolerably 
water  tight ;  and  the  water  which  does  make  its  way 
through  the  walls,  or  which  springs  out  of  the  en- 
closed bed,  is  drawn  off  by  pumps  and  hand  labor, 
or,  if  the  undertaking  be  considerable,  by  means  of 
a  steam  engine. 

Besides  bridges,  other  bodies  of  masoiu'y  are  also 
requisite,  if  not  completely  to  transverse,  at  least  to 
advance,  a  considerable  way  into  the  water.  Such 
are  the  moles  and  piers  carried  out  from  the  land 
into  the  sea,  from  opposite  points  of  the  shore,  and 
mutually  bending  round  towards  each  other  at  their 
extreme  points,  where  they  leave  an  interval  suffi- 
cient for  the  passage  of  ships  out  or  in.  In  our  seas, 
where  we  have  the  advantage  of  the  retreat  of  the 
sea  twice  a  day,  at  low  water  such  structures  can  be 


30 


INTRODUCTION. 


founded  and  carried  up,  in  general,  without  partic- 
ular difficulty.  In  the  Mediterranean,  however,  where 
the  rise  and  fall  of  the  tide  is  either  very  unimpor- 
tant or  wholly  insensible,  —  as  along  the  coasts  of 
Spain,  France,  Italy,  &:c., — the  construction  of  a  mole 
becomes  an  enterprise  of  vast  labor,  difficulty,  and 
expense. 

The  work  begins  at  the  shore,  by  throwing  into 
the  sea  blocks  of  rock  or  stone,  the  larger  the  more 
useful.  These  find  thcii-  place  in  the  bottom,  and, 
by  accumulating  block  upon  block  over  them,  they 
at  last  rise  above  the  surface  of  the  water.  The 
work  being  so  far  advanced,  advantage  is  taken  of 
the  blocks  above  water  to  form  a  road,  by  which 
other  blocks  arc  carried  out  and  rolled  into  the  sea 
beyond  those  akeady  placed,  and  these  again  in  their 
turn  serve,  when  they  come  to  the  surface,  to  convey 
another  succession  of  blocks,  until  the  foundation  of 
the  mole  be  earned  out  to  the  intended  extent.  When 
we  take  into  consideration  the  inequalities  of  the 
bottom  of  the  sea,  where  not  covered  with  hard  sand, 
the  incessant  internal  motion  of  the  waters,  produced 
by  currents,  to  say  nothing  of  the  superficial  agita- 
tion produced  by  the  winds,  that  most  rocks  and 
stones  lose  a  great  part  of  theu-  weight  when  im- 
mersed in  salt  water,  —  and  are,  consequently,  more 
easily  moved  about  from  place  to  place  by  the  mo- 
tion of  the  waters,  —  also  the  gi-cat  extent  in  breadth 
to  which  rude  blocks  of  stone  or  rock  will  necessa- 
rily roll  before  they  find  a  bed,  cither  in  the  bottom 
of  the  sea,  or  on  one  another,  —  when  all  these  things 
are  considered,  the  structure  of  moles  and  piers  in 
such  seas  must  appear  to  be  an  enterprise  of  extreme 
difficulty  and  expense.  In  siich  seas,  however,  no 
other  mode  of  consti-ucting  an  artificial  harbor  can 
be  devised.  When  the  foundation  is  supposed  to  be 
sufficiently  consolidated,  and  is  raised  above  the 
aurface  of  the  water,  the  mole  is  completed  by  a 
structure  of  hewn  stone,  founded  in  the  interstices  of 
the  sunk  blocks,  adapted  to  the  purposes  of  com- 
mercial and  maritime  affairs.  Of  this  constriiction 
are  the  old  and  new  models  of  Gibraltar,  of  Alicant, 
Tarragona,  and  Barcelona,  in  Spain  ;  of  Sette  and 
Toulon,  in  France ;  of  Genoa,  Leghorn,  Civita 
-^  Vecchia,  Naples,  and  Anchona,  in  Italy,  (S:c.  The 
famous  antique  mole  at  Pozzuoli,  in  tlic  Bay  of 
Naples,  is  constructed  with  piers  and  arches  founded 
in  the  sea,  and  is,  fi-om  its  appearance,  called  Calig- 
ula's Bridge,  having  been,  as  is  supposed,  erected  by 
that  imperial  monster.  On  the  same  principles  with 
the  moles  just  described  is  consti-uctcd  what  is  called 
the  Breakwater,  in  the  enti-ancc  of  Plymouth  Haven, 
in  England,  in  the  view  of  abating  "the  violence  of 
the  waves  and  currents  which  have,  on  many  occa- 
sions, proved  most  prejudicial  to  the  fleets  resorting 
to  that  otherwise  admirable  station  for  shipping  of 
every  sort.  In  the  report  laid  before  the  British 
Parliament    concerning   this    prodigious    enterprise, 


which  was  earned  on  at  the  public  expense,  the  en- 
gineers, Messrs.  Rennie  and  Whitby,  (the  former  the 
engineer  for  the  Strand  Bridge,  in  London,)  state 
that  tliere  are,  properly  spealdng,  tliree  entrances  into 
Plymouth  Sound  or  Haven,  viz.,  one  on  the  west 
side  of  the  bay,  bounded  by  a  long  cluster  of  small 
rocks,  called  Scott's  Ciround,  and  the  depth  is  only 
from  3  to  4  fathoms,  (fi-om  18  to  24  feet,)  at  low 
water ;  and  on  the  east  by  the  Knap  and  Panther, 
on  which  is  about  the  same  depth  of  water.  This 
channel  is  about  500  fathoms  wide,  and  the  general 
depth  is  from  5J  to  6  fathoms  at  low  water.  The 
middle  channel  is  bounded  by  the  Knap  and  Panther 
on  the  west,  and  by  tlie  Tinker  and  Shovel  on  the 
cast ;  about  300  fathoms  wide,  and  the  general  depth 
from  6i  to  8  fathoms,  at  low  water. 

From  this  description,  it  appears  that  a  large  part 
of  the  middle  of  Plymouth  Sound  is  shut  up  by  the 
Shovel  and  St.  Carlos's  Rocks ;  that  is,  as  a  channel 
for  large  ships.  Of  com'sc,  works  erected  on  those 
rocks  would  be  no  obstruction  to  a  passage  in  or  out 
of  the  Sound.  If  a  pier  or  breakwater  were  con- 
structed on  the  Shovel  Rocks,  and  extended  west- 
ward, so  as  to  shut  up  in  part  the  channel  between 
them  and  the  Panther,  and  also  to  shut  up  or  narrow 
the  spaces  between  St.  Carlos's  Rocks  and  Andurn 
Point,  the  tide  being  then  confined  to  a  naiTow  space, 
the  velocity  of  the  current  would  be  increased,  and, 
consequently,  the  channels  where  it  passed.  It 
seemed,  therefore,  proper  that  a  pier  or  breakwater 
should  be  constructed  in  the  Sound,  having  its  east- 
ern end  about  60  fathoms  east  from  St.  Carlos's 
Rocks,  and  its  western  end  about  300  fathoms  west 
from  the  Shovel,  forming,  in  the  whole,  a  length  of 
850  fathoms.  Of  this  pier,  500  fathoms  in  the  mid- 
dle should  be  straight,  and  175  at  each  end  inclined 
at  an  angle  of  120  degi-ccs.  In  addition  to  this 
breakwater,  another  should  be  extended  fi-om  Andurn 
Point,  on  tlie  shore,  towards  the  former,  of  about  400 
fathoms  in  length,  having  also  a  part  inclined  at  an 
equal  angle.  These  inclined  parts  were  to  repel  the 
waves  in  such  a  manner  as  to  prevent  them  from 
passing  violently  through  the  opening  between  the 
piers,  and  to  shelter  tlie  Sound  within,  so  as  to  permit 
fifty  sail  of  line-of-battle  ships  to  ride  at  anchor  in 
safety,  in  all  winds  and  weather,  and  with  ample 
room  to  work  thek  way  out  to  sea,  by  one  or  other 
of  the  channels,  as  then-  position  and  state  of  the 
wind  might  render  most  convenient. 

These  great  works  were  to  be  constructed  by  large 
blocks  of  stone  thrown  at  random  into  the  sea,  in  the 
line  of  the  intended  breakwater,  to  find  their  own 
bed.  Stones  from  a  ton  and  a  half  to  two  tons  in 
weight  would  probably  resist  the  swell  of  the  Sound, 
in  stormy  weather.  Where  the  water  is  five  fathoms 
deep,  the  base  of  the  breakwater  should  not  be  less 
than  seven  times  that  depth,  or  seventy  yards  in 
breadth,  and  ten  yards  broad,  at  a  height  of  ten  feet 


INTRODUCTION. 


31 


above  the  level  at  low  water  or  ordinary  spring  tides. 
The  slope  of  this  foundation  on  tlio  outer  side,  next 
to  the  sea,  should  be  in  tlic  proportion  of  three  yards 
horizontal  for  one  yard  perpendicular ;  but  the  slope 
on  the  inside,  next  tlie  Sound,  would  require  an  in- 
clination of  only  half  that  quantity,  or  one  and  a 
half  yards  horizontal  for  one  yard  perpendicular.  To 
the  project  here  described  (and  now  completed) 
various  objections  were  made,  particularly  by  Mr. 
Bentham,  who  had  executed  some  works  at  Shecr- 
ness,  at  the  conflux  of  the  Thames  and  the  jNIedway, 
somewhat  of  the  same  nature,  but  in  circumstances 
incomparably  more  easy  to  manage  than  in  the  open, 
stormy  entrance  at  Plymouth  Sound.  He  observed 
that  such  a  work  as  that  proposed  by  Messrs.  Rennie 
and  Whitby,  even  supposing  sufficient  precaution  to 
have  been  taken  to  prevent  any  injury  to  the  harbor 
during  its  execution,  and  that  the  whole  were  com- 
pleted in  its  gi'catcst  perfection,  would,  nevertheless, 
by  opposing  throughout  its  extent  a  complete  inter- 
ruption to  the  water,  occasion  such  eddies  in  the 
wake  of  the  work,  and  such  an  increased  action  on 
the  bottom  and  sides  of  the  parts  left  open,  as  could 
not  fail  of  forming  shoals,  more  or  less  injurious, 
according  to  the  nature  of  the  soil  and  other  local 
ch-cumstances.  Mr.  Bentham's  plan  was  to  sink  in 
the  sea,  but  in  a  line  of  dkection  difterent  from  that 
of  the  other  engmeers,  a  double  row  of  cylincbical 
masses  of  stone  work,  leaving  an  interval  between 
each  two  masses  above  equal  to  their  diameter; 
placing  the  masses  in  one  row  opposite  to,  and  cover- 
ing the  intervals  between,  the  masses  in  the  other 
row.  By  this  an-angement,  while  the  two  rows  in 
conjunction  formed  a  complete  obstacle  to  the  dii-ect 
course  of  the  waves,  tlie  tide  or  current  would  be 
allowed  to  pass  freely  between  the  masses,  through- 
out the  whole  extent  of  the  breakwater ;  boats  also, 
and  even  small  vessels,  might,  in  moderate  weather, 
pass  through  the  intervals  without  danger.  Notwith- 
standing these  objections  and  proi>osals,  the  scheme 
of  Messrs.  Rennie  and  Whitby,  all  circumstances 
duly  balanced,  was  adopted  by  government,  and  or- 
dered to  be  earned  into  effect.  On  a  plan  much  of 
the  kind  proposed  by  Mr.  Bcnham,  was  begun  in 
France,  before  the  revolution,  a  project  for  forming 
an  artificial  roadstead,  or  place  of  anchorage  for  ships 
of  war,  in  fi-ont  of  Cherbourg,  on  the  north  coast  of 
Normandy.  This  place,  situated  in  the  bottom  of  a 
wide,  open  bay,  on  a  part  of  the  coast  projecting 
considerably  into  the  British  Channel,  lies  only  about 
sixty  miles  south  from  the  Isle  of  Wight,  and,  tliere- 
fore,  offers  a  most  advantageous  position  for  watching 
the  motions  of  British  fleets  moving  up  and  down 
the  channel,  or  proceeding  from  or  into  the  great 
place  of  rendezvous  at  Portsmouth  or  Spithead. 
Cherbourg  possesses  no  natural  qualifications  for  a 
shipping  station,  being  merely  a  tide  harbor  formed 
by  a  small  river  falling  into  the  sea.     Basins  ha->'e 


been  excavated  and  locks  constructed,  in  former 
times,  by  means  of  which  frigates  and  smaller  vessels 
could  be  conveniently  protected ;  all  with  uncommon 
ingenuity,  and  at  a  very  moderate  expense.  It  was 
not  enough  for  an  engineer  in  France  to  give  proof 
of  his  genius  and  skill  in  his  profession,  in  producing 
the  best  method  of  accomplishing  any  desired  object ; 
his  great  merit  consisted  in  inventing  how  to  accom- 
plish that  object  in  the  most  economical,  as  well  as 
the  most  iiig-enious,  manner.  By  giving  this  turn  to 
the  public  mind,  works  of  the  highest  importance  to 
the  state  and  to  individuals  were  carried  on,  in  that 
country,  for  sums  which,  in  some  other  countries, 
would  be  regarded  as  utterly  inadequate  to  the  pur- 
pose. All  persons  charged  with  the  execution  of 
public  works,  even  those  we  call  civil  engineers,  em- 
ployed in  the  construction  of  harbors,  bridges,  canals, 
roads,  &c.,  were  military  men,  regularly  bred,  and 
under  due  but  liberal  control,  enjoying  rank  and 
emolument  sufficient  for  their  station  in  society.  An 
instance  of  a  superior  officer  of  the  French  corps  of 
Royal  Engineers  suspected,  accused,  tried,  and  con- 
victed of  recommending  works  which  he  well  knew 
to  be  unnecessary,  not  to  say  prejudicial,  that  he 
might  have  an  opportunity  of  enriching  himself  dur- 
ing theu-  execution ;  or  of  conniving  at,  not  to  say 
inventing,  enormous  abuses  and  extravagant  expendi- 
ture, in  the  management  of  the  public  moneys,  in 
order  that  he  might  be  suffered,  by  the  plunderers 
under  him,  quietly  to  amass  his  ti'easures  ;  that  a  field 
officer  of  engineers  should  be  proved  to  have  stooped 
so  low  as  even  to  make  false  returns  of  the  quantity 
of  coals  and  candles  necessary  for  his  official  busi- 
ness, —  an  instance  of  such  degrading  delinquency  is 
unknown  in  the  history  of  French  military  jurispru- 
dence. How  far  the  same  remark  can  be  applied  to 
another  country,  the  constant  rival,  and  often  the  en- 
emy, of  France,  the  records  of  the  courts  which  take 
cognizance  of  such  offences  against  duty,  honor,  and 
even  common  honesty,  will  bear  ample  Ijut  humiliat- 
ing testimony.  As  Cherbourg  possessed  no  outer 
harbor  or  road  such  as  Portsmouth  possesses  at  Spit- 
head,  it  became  necessary  to  enclose  a  portion  of  the 
bay  to  answer  that  purpose.  Piers  or  breakwaters 
of  continued  construction  were  thought  of;  but  at 
last  it  was  resolved  to  sink  a  long  range  of  wooden 
truncated  cones  into  the  sea  at  certain  distances 
asunder,  which,  being  afterwards  filled  with  massy 
blocks  of  stone,  would  form  a  succession  of  solid, 
immovable  masses,  sufficient  to  break  the  violence 
of  the  external  waves,  and  render  the  space  within 
incomparably  more  quiet  and  secure  than  it  was 
in  its  natural  state.  The  cones  were  strongly  com- 
pacted of  oak,  narrower  above  than  below,  and  re- 
sembling a  deep  tub  standing  on  its  base,  w^ithout  a 
bottom.  By  most  ingenious  contrivances,  the  cones 
were  floated  out  to  their  destined  situations  by  means 
of  empty  casks,  made  air  tight,  which  were  afterwards 


32 


INTRODUCTION. 


detached,  and  the  frame  allowed  to  sink  to  the  bot- 
tom. The  sides  were  of  sufficient  height  to  be 
always  above  water,  and,  when  filled  with  stone, 
withstood  the  action  of  the  tide  and  waves. 

This  great  enterprise,  the  only  thing  of  the  kind  in 
the  world,  was  naturally  interrupted  by  the  disorders 
of  the  revolution  in  France,  but  was  afterguards  re- 
sumed with  great  activity,  so  that,  in  future  wars  with 
France,  Cherbourg  may  become  a  most  troublesome 
neighbor  to  Britain. 

WOODEN  BRIDGES. 

Besides  stone,  timber  is,  on  many  occasions,  em- 
ployed to  open  a  communication  across  a  river  ;  and 
in  some  cases  it  has  greatly  the  advantage,  as  when 
the  current  is  particularly  rapid ;  for  there  the  posts 
or  piles  supporting  the  road,  presenting,  either  indi- 
vidually or  collectively,  but  a  small  obstacle  to  the 
stream,  often  effectually  resist  its  violence,  when  a 
stone  pier,  if  it  could  easily  be  constructed  in  such  a 
position,  would  not  long  keep  its  ground.  Hence  it 
is,  that  not  only  in  England,  but  more  particularly 
on  the  continent,  stone  bridges  over  great  rivers  are 
comparatively  rare.  Thus,  on  the  Rhone,  for  in- 
stance, which,  rising  in  the  highest  Alps  of  Switzer- 
land, makes  its  way  to  the  sea  through  the  southern 
parts  of  France,  bridges  of  stone  have  often  been 
constructed,  and  as  often  carried  away  by  the  stream, 
so  that  at  this  day,  perhaps,  not  more  than  two  re- 
main. The  Rhone  is,  however,  the  most  rapid  river 
of  its  size  in  Europe.  On  the  Rhine,  which,  rising 
not  far  from  the  source  of  the  Rhone,  takes  an  oppo- 
site course  through  Germany  and  Holland  into  the 
German  Ocean,  and  is  so  much  less  rapid  as  its 
course  is  longer,  stone  bridges  are  quite  unknown. 
But  this  is  owing  not  only  to  the  great  body  of  water 
it  carries  along,  but  also  to  the  policy  of  the  different 
states  along  its  banks,  each  unwilling  that  the  oppo- 
site state  should,  by  a  standing  bridge  of  masonry, 
possess  means  of  making  hostile  attempts  across  the 
river.  At  Strasbiu-g,  for  instance,  a  large  and  pros- 
perous city  of  Alsace,  in  France,  seated  on  the  west 
bank  of  the  Rhine,  commanding  by  its  fortifications 
a  much  frequented  passage  over  the  river  into  Ger- 
many, the  bridge  is  formed  by  ranges  of  pUes  driven 
into  the  river  to  form  the  piers,  supporting  rafters  and 
planks  for  the  road,  kept  in  their  place  by  wooden  bolts 
or  treenails,  so  that,  with  a  few  strokes  of  a  hammer  or 
hatchet,  the  planks  could  be  cast  loose  and  removed, 
and  all  passage  along  the  bridge  effectually  cut  off. 
The  German  end  of  the  bridge  was  also  guarded  by 
works  to  prevent  the  French  from  penetrating  by  that 
communication.  This  is  the  bridge  of  Kehl,  cele- 
brated in  every  history  of  hostilities  between  France 
and  Germany. 

Various  arc  the  methods  employed  in  the  construc- 
tion of  wooden  bridges,  governed  principally  by  the 


extent  of  water  they  are  to  cross.  Even  in  the  nar- 
rowest it  is  improper  to  trust  to  the  resistance  of 
beams  reaching  from  bank  to  bank,  for  they  ought  to 
be  trussed ;  that  is,  to  be  supported  by  pieces  of  tim- 
ber reaching  from  each  bank,  near  the  water,  obliquely 
towards  the  middle  of  the  bridge.  This  contrivance 
will  add  greatly  to  its  strength,  and  prevent  its  bend- 
ing under  passing  loads. 

One  of  the  most  important  particulars  to  be  con- 
sidered, in  wooden  bridges,  is  the  seasoning  of  the 
timber.  It  is  well  known  that  the  decay  of  fir  timber 
is  generally  owing  to  the  moist,  sappy  nature  of  its 
exterior  surface.  This  moisture  must  be  completely 
removed  before  any  paint  or  priming  be  applied,  in 
the  view  of  securing  it  from  the  weather.  K  left  in 
this  natural  state,  this  sap  would,  by  the  action  of 
the  wind  and  heat,  be  gradually  carried  off,  and  the 
fir  beam  become  internally  dry  and  solid  ;  but  if  the 
surface  be  covered  with  paint,  oil,  pitch,  or  other  sub- 
stances of  this  kind,  the  sap  is  confined,  and  will  soon 
corrupt  the  timber,  which  wUl  give  way  before  its 
time,  and  without  any  external  symptom  of  decay. 
In  order  to  dissipate  the  moisture  or  sap  of  the  sur- 
face, it  is  sometimes  the  practice  to  scorch  the  tim- 
bers over  a  fire,  turning  it  round  regularly.  The  heat 
will  attract  the  moisture  to  the  surface  and  evaporate 
it,  and  the  timber  will  acquire  a  hard  crust,  of  great 
service  in  resisting  the  weather.  When  this  is  done, 
the  parts  that  are  to  be  under  water  shotild  be  care- 
fully covered  with  pitch  and  tar,  sprinkled  with  sand 
and  powdered  shells.  Those  which  are  in  sight 
should,  while  the  wood  is  still  hot  from  the  fire,  be 
rubbed  over  with  linseed  oil,  mLxed  with  a  little  tar, 
which  will  then  strike  deep  into  the  wood,  and  soon 
become  so  hard  as  to  be  fit  to  paint.  Fii'  timber,  thus 
prepared,  is  found  to  be  nearly  equal  to  oak  in  dura- 
bility. At  Schaffhausen,  in  the  north  part  of  Swit- 
zerland, was  once  to  be  seen  a  wooden  bridge  over 
the  Rhine,  there  very  rapid,  so  that  no  stone  bridge 
could  resist  it — admirable  in  its  construction,  and  be- 
ing the  production  of  a  plain  country  carpenter.  The 
builder  was  directed  to  avail  himself  of  a  part  of  one 
of  the  piers  of  the  stone  bridge  still  remaining  in  its 
place,  to  support  the  intended  structure.  With  this 
order  he  apparently  complied,  but  so  conti'ived  mat- 
ters that,  in  the  opinion  of  the  best  judges,  his  bridge 
actually  consisted  of  but  one  immense  arch,  of  near 
four  hvmdred  feet,  (the  breadth  of  the  river,)  having  a 
part  stooping  down,  as  it  were,  to  rest  upon  the  pier 
in  the  water,  but  not,  as  far  as  coiold  be  discovered, 
actually  resting  on  it.  With  very  long  fir  beams, 
prepared  for  the  pvirpose,  extended  at  an  angle  of  mod- 
erate elevation  above  the  horizon  from  both  sides  of 
the  river,  and  in  conjunction  with  intermediate  tun- 
bers,  meeting  over  the  water,  two  arches  were  formed, 
being  segments  of  large  circles,  and  resembling  the 
circular  frame  of  the  centring  of  a  stone  bridge. 
These   arches  were  placed  parallel  to  one  another, 


INTRODUCTION. 


33 


at  a  distance  sufficient  for  the  breadtli  of  the  road, 
which  was  formed  upon  timbers  suspended  from  the 
arches  on  each  side,  so  as  to  be  quite  horizontal  from 
end  to  end ;  and,  instead  of  going  over  the  supporting 
arches,  was,  in  fact,  let  down  between  them.  The 
whole  was  roofed  over,  and  enclosed  at  the  sides, 
with  windows  at  convenient  distances  to  defend  the 
timber  from  the  weather.  This  most  ingenious  and 
most  useful  piece  of  carpentry,  which  had  gained  the 
applause  of  all  men  of  genius  and  skill,  completely 
answered  its  destination  from  1740,  when  it  was 
constructed,  to  1799,  when  it  was  destroyed  by  the 
French. 

IRON  BRIDGES. 

Bridges  of  iron  are  the  production  of  British  inge- 
nuity exclusively.  Iron  being  the  great  staple  metal 
of  the  country,  it  has  of  late  been  employed  in  many 
works  where  great  strength  is  required  in  proportion 
t6  the  weight  of  the  materials.  Melted  or  cast  iron 
possesses  several  advantages  over  stone  or  wood ;  and 
these,  in  their  turn,  possess  advantages  over  cast  iron. 
To  stone,  iron  is  superior  in  tenacity  and  elasticity, 
and  thence  in  strength,  in  facility  of  formation  in  any 
desired  shape,  and  in  extent  of  the  masses  in  which 
it  may  be  formed  —  qualities  all  conducing  to  its 
superior  lightness  and  cheapness.  To  wood,  iron  is 
superior  in  the  same  particulars,  together  with  dura- 
bility ;  but  in  this  last  respect,  stone  has  greatly  the 
advantage  over  iroii  equally  exposed  to  the  weather 
or  other  natural  agents.  The  greater  durability  of 
stone  arises  from  its  being  less  liable  to  decomposi- 
tion from  the  atmosphere,  and  from  its  being  less 
elastic,  and  consequently  less  subject  to  friction  among 
its  component  particles,  in  yielding  to  the  load  and 
motion  of  carriages  passing  over  it.  Several  ways 
may,  however,  be  adopted  to  remedy,  in  a  great  de- 
gree, these  defects  of  iron.  Paint  will  prevent  it  from 
oxidation,  or  rusting,  for  many  years,  and  the  appli- 
cation may,  when  necessary,  be  repeated  without 
much  expense.  Cast-iron  carriages  of  garrison  guns 
have,  by  various  external  applications,  been  perfectly 
preserved  for  upwards  of  a  century.  The  vibratory 
motion  of  an  iron  bridge  may  also  be  considerably 
diminished  by  the  manner  of  placing  and  connecting 
the  bars  of  which  it  consists,  so  that  each  bar  shall 
act  as  nearly  as  possible  at  right  angles  against 
another,  and  be  at  the  same  time  so  short  as  not  to 
be  in  danger  of  being  bent  or  crushed  by  the  pressure 
against  its  length.  The  greatest  objection  in  this 
respect  to  cast  iron  is  this  —  that,  on  account  of  the 
imperceptible  differences  in  the  purityand  other  qual- 
ities of  the  metal,  it  is  impossible  to  cast  two  bars  or 
blocks  even  in  the  same  mould,  which  shall  shrink 
perfectly  and  equally  in  cooling,  and,  consequently,  be 
of  precisely  the  same  dimensions  when  employed  in 
the  work.     When  such  pieces  come  to  be  joined  to- 


gether, therefore,  some  empty  space  must  necessarily 
exist  among  them,  which  in  a  large  work,  where  uianv 
pieces  are  employed,  must  produce  a  very  sensible 
play  in  the  joinings,  and,  consequently,  great  vibration 
or  reciprocal  motion  in  the  whole  structure.  This 
inaccuracy  of  the  joinings  may,  it  is  true,  be  in  some 
measure  corrected,  by  inserting  pieces  of  sheet  lead 
in  the  joinings;  but  this  metal  possesses  by  far  too 
little  cohesion  of  parts,  and  too  little  elasticity,  to  be 
of  use  for  any  length  of  time.  In  order  to  prevent 
the  evils  arising  from  these  defects  of  cast  iron,  it  has 
been  proposed  to  fill  up  the  vacant  spaces  left  be- 
tween the  iron  framing  with  some  compact,  cheaj) 
materials,  such  as  brick  united  with  the  composition 
called  Roman  or  Parke's  cement,  or  Pozzolano,  or 
terras,  which  would  readily  and  intimately  combine 
with  the  iron,  thus  defending  it  from  the  action  of 
the  atmosphere.  The  interstices  between  the  bars 
being  thus  also  filled  up  by  a  consolidated  substance, 
the  play,  friction,  and  vibratory  motion  of  the  bridge 
would  be  greatly  diminished.  Lightness  being,  how- 
ever, a  most  desirable  property,  it  has  also  been  pro- 
posed to  form  hollow  bricks  solely  for  this  purpose, 
which,  being  carefully  and  thoroughly  baked,  or  even 
semi-vitrified  on  the  surface,  would  be  proof  against 
the  effects  of  the  atmosphere.  In  many  parts,  bricks 
are  still  seen  in  remains  of  Roman  buildings,  fifteen 
or  sixteen  hundred  years  old  in  perfect  preservation, 
while  the  stones,  with  which  the  bricks  are  buOt  up 
in  alternate  layers,  are  often  greatly  decayed,  unless 
when  enveloped  in  the  admirably-constituted  mortar 
of  those  days.  Iron  may  be  used  for  bridges,  either 
on  the  principle  of  equilibration,  as  stone  is  employed, 
or  on  that  of  connection  by  framing,  as  wood  is  some- 
times employed  in  bridges,  but  generally  in  roofing 
houses.  For  bridges  of  considerable  dimensions  the 
former  is,  by  many  judges,  esteemed  the  best  mode ; 
but  for  small  bridges,  the  latter  mode  will  probably 
be  found  the  cheapest.  As  iron  bars,  rods,  or  blocks 
may  be  firmly  connected  together  by  bolts,  or  other 
means,  an  iron  arch  may  be  constructed  much  flatter ; 
that  is,  in  the  segment  of  a  much  greater  circle  than 
if  it  were  of  stone  —  an  advantage  of  very  great  im- 
portance in  certain  positions,  where  arches  of  great 
span  are  required.  The  first  iron  bridge  of  any  note 
constructed  in  England  was  that  of  Colebrookdale, 
in  Shropshire.  It  consists  of  five  ribs,  each  of  three 
concentric  arches,  bound  together  by  pieces  in  the 
direction  of  radii  of  the  circle.  The  interior  arch 
forms  a  semicircle,  but  the  others  reach  only  to  sills 
under  the  road  way.  These  arcs  pass  through  an  up- 
right frame  of  iron  at  each  end,  serving  as  a  guide ; 
and  the  small  space  in  the  haunches,  between  the 
frames  and  outer  arc,  is  filled  up  with  a  large  iron 
ring.  On  the  ribs  are  laid  cast-iron  plates,  to  support 
the  road.  The  span,  or  opening  of  the  arch,  is  100 
feet  6  inches,  and  the  height  from  the  base  line  to  the 
centre  is  40  feet.     The  road  along  the  bridge  is  24 


34 


INTRODUCTION. 


feet  broad,  formed  on  a  bed  of  clay  and  iron  slag, 
(the  refuse  from  the  furnace  where  iron  ore  is  smelted,) 
a  foot  in  depth. 

Another  bridge  of  the  same  material  was  after- 
wards erected  over  the  mouth  of  the  River  Were,  form- 
ing the  Harbor  of  Sunderland,  a  great  coal  port  in  the 
county  of  Durham.  The  peculiar  construction  of 
this  bridge  consisted  in  applying  iron,  or  other  metal- 
lic substance  or  compound,  to  form  arches  on  the 
same  principle  with  stone  arches,  by  a  subdivision 
into  blocks  easily  portable,  answering  to  the  key- 
stones of  a  common  arch,  which,  being  made  to  bear 
on  one  another,  will  have  all  the  firmness  of  a  stone 
arch.  At  the  same  time,  by  the  great  open  spaces 
left  between  the  blocks  and  their  respective  lateral 
distances,  the  arch  becomes  materially  lighter  than 
if  it  were  of  solid  stone,  and,  by  the  tenacity  of  the 
metal,  the  parts  are  so  intimately  connected  that  the 
delicate  but  indispensable  calculation  of  the  size  and 
weight  of  the  stones  composing  the  arch  becomes  of 
but  little  importance.  This  bridge  is  in  span  236 
feet,  and  as  the  stones  from  which  the  arch  springs 
on  each  side  project  2  feet,  the  whole  opening  is  240 
feet.  The  arch  is  a  segment  of  a  circle  of  222  feet 
radius,  and  the  height  from  the  chord  to  the  top  of 
the  arch  is  34  feet ;  but  the  whole  height  of  the  mid- 
dle of  the  arch  above  the  surface  of  the  river,  at  low 
water,  is  about  100  feet,  so  that  ships  can  pass  under 
it.  A  series  of  105  blocks  form  one  rib,  and  six  of 
such  ribs  compose  the  width  of  the  bridge.  The  va- 
cant spaces  between  the  arch  and  the  road  are  filled 
up  by  cast-iron  circles,  which  touch  the  outer  circum- 
ference of  the  arch,  and  also  support  the  road,  grad- 
ually diminishing  from  the  abutments  towards  the 
centre  of  the  bridge.  Diagonal  iron  bars  are  laid  on 
the  top  of  the  ribs,  reaching  to  the  abutments,  to  keep 
the  ribs  from  twisting.  The  supersti-ucture  is  a  strong 
frame  of  timber,  planked  over  to  support  the  carriage 
road,  composed  of  marble,  limestone,  and  gravel,  with 
a  cement  of  tar  and  chalk  laid  on  the  planks  in  order 
to  preserve  them.  The  whole  width  of  the  bridge  is 
32  feet.  The  abutments  are  masses  almost  of  solid 
masonry,  24  feet  in  thickness,  42  in  breadth  at  the 
bottom,  and  37  at  the  top.  The  weight  of  the  iron 
in  the  whole  work  is  260  tons,  of  which  214  are  cast, 
and  42  wrought  iron.  The  expense  of  the  whole, 
forty  years  ago,  was  £27,000,  or  $119,880.  The 
Waterloo  Bridge,  over  the  Thames,  will  be  illustrated 
by  a  plate  for  that  purpose. 

BRIDGES  IN  BOSTON. 

Some  of  the  most  striking  objects  which  attract 
the  notice  of  strangers  on  visiting  Boston,  Massachu- 
setts, are  the  bridges  which  lead  from  its  various 
points.  Although  wc  cannot  boast  of  so  grand  su- 
perstructures as  the  ancient  city  of  London,  we,  nev- 
ertheless, have  a  greater  number  of  those  convenient 


avenues.  The  Western  Avenue  is  a  splendid  mill 
dam,  built  of  solid  materials.  Warren  Bridge  was 
built  in  1828.  All  these  bridges  are  well  lighted  by 
lamps  when  the  evenings  are  dark  ;  and  the  lights, 
placed  at  regular  distances,  have  a  splendid  and 
romantic  appearance. 

WESTERN   AVENUE. 

This  splendid  work  was  projected  by  Mr.  Uriah 
Cotting,  who,  with  others  associated,  received  an  act 
of  incorporation,  June,  1814,  under  the  title  of  "  The 
Boston  and  Roxbury  Mill  Corporation."  It  was  com- 
menced in  1818,  under  Mr.  Cotting's  direction,  but  he 
did  not  live  to  witness  its  completion.  His  place  was 
supplied  by  Colonel  Loammi  Baldwin,  and  the  road 
was  opened  for  passengers  July  2, 1821.  This  Avenue, 
or  Mill  Dam,  leads  from  Beacon  Street,  in  Boston,  to 
Sewall's  Point,  in  Brookline,  and  is  composed  of  solid 
materials,  water-tight,  with  a  gravelled  siuface,  raised 
three  or  four  feet  above  high-water  mark.  It  is  one 
mile  and  a  half  in  length,  and  a  part  of  the  way  100 
feet  in  width.  The  water  which  is  admitted  is  ren- 
dered subservient  and  manageable.  Very  extensive 
mill  privileges  are  gained  by  the  aid  of  a  cross  dam, 
running  from  the  principal  one  to  a  point  of  land  in 
Roxbury,  which  divides  the  reservoir  or  full  basin  on 
the  west  from  the  running  or  empty  basin  on  the 
east.  There  are  five  pairs  of  floodgates  in  the  long 
dam,  grooved  in  massy  piers  of  hewn  stone  ;  each 
pair  moves  from  their  opposite  pivots  towards  the 
centre  of  the  aperture  on  a  horizontal  platform  of 
stone,  lentil  they  close  in  an  obtuse  angle,  on  a  pro- 
jected line  cut  on  the  platform,  from  the  pivots  in  the 
piers  to  the  centre  of  the  space,  with  thefr  angular 
points  towards  the  open  or  iincnclosed  part  of  the 
bay,  to  shut  against  the  flow  of  tide,  and  prevent  the 
passage  of  water  into  the  empty  basin.  In  this  man- 
ner, all  the  water  is  kept  out  from  this  basin,  except 
what  is  necessary  to  pass  from  the  full  basin  through 
the  cross  dam,  to  keep  the  mill  works  in  operation. 
The  reservoir  is  kept  full  by  means  of  similar  flood- 
gates opening  into  the  full  basin,  (when  the  rising 
of  the  tide  gets  ascendency  over  the  water  in  the 
reservoir,)  and  fills  at  every  flow,  and  closes  again  on 
the  receding  of  the  tide.  In  this  way,  at  every  high 
tide,  the  reservoir  is  filled,  and  a  continual  supply  of 
water  is  made  to  pass  through  the  sluice  ways  in  the 
cross  dam,  sufficient  to  keep  in  motion,  at  all  times, 
at  least  one  hundred  mills  or  factories.  At  low 
water,  the  floodgates  of  the  receiving  basin  open  and 
discharge  the  water  received  from  the  reservoir. 

WARREN   BRIDGE. 

The  construction  of  this  bridge  was  commenced  in 
June,  1828,  and  was  completed  in  November  follow- 
ing, under  the  superintendence  of  Joshua  Burr,  Esq., 


INTRODUCTION. 


of  Cliurlestown,  Massachusotts.  It  is  one  of  the  most 
pertect  works  of  its  kind  in  the  Commonwealth.  It  is 
certainly  not  exceeded  by  any  other  in  point  of  dura- 
bility and  ease  of  travel.  It  opens  on  the  Charles- 
town  side,  about  ten  rods  above  (west)  Charles  River 
Bridge,  and,  running  in  a  southerly  direction,  termi- 
nates on  the  westerly  part  of  the  Will  Pond  Land,  so 
called,  in  Boston,  just  east  of  the  Middlesex  Canal. 
It  is  the  most  direct,  and  the  shortest,  communication 
between  Boston  and  Charlestown. 

The  bridge  is  supported  by  75  piers,  placed  at 
equal  distances  of  18  feet.  It  is  1390  feet  in  length, 
and  44  in  width,  allowing  30  feet  for  the  carriage 
way,  and  6^  on  either  side,  handsomely  railed,  for 
foot  passengers.  The  floor  of  tlie  bridge  is  composed 
of  hewn  hemlock  timber,  about  14  inches  deep,  the 
apertm-es  between  which  arc  well  chinked  with  small 
pieces  of  stone,  the  whole  covered  with  6  inches  of 
tempered  clay.  On  this  is  spread  8  inches  of  coarse 
gravel,  covered  with  8  inches  of  macadamized  stone. 
The  sides  of  the  carriage  way  are  secured  by  edge 
stones,  12  inches  deep  and  9  thick.  The  floor  tim- 
bers are  placed  lower  than  those  of  other  bridges,  in 
order  that  they  may  be  occasionally  wet  by  the  high 
tides,  which,  it  is  thought,  will  tend  to  their  preser- 
vation. That  teams  pass  over  this  bridge  with  great 
ease  is  sufficiently  demonstrated  by  the  fact  that  a 
single  yoke  of  oxen  has  been  known  to  convey  161 
tons  at  one  time,  from  the  draw  into  Charlestown, 
without  any  unusual  effort. 

The  draw,  in  the  centre  of  the  bridge,  is  of  suffi- 
cient width  to  admit  vessels  of  three  hundred  tons. 
It  has  wharves  on  each  side,  built  on  piers  which  are 
planked  from  the  capsill  to  low-water  mark,  for  the 
more  safe  and  easy  passage  of  vessels.  Its  con- 
veniences, in  this  particular,  are  in  strict  agreement 
with  the  general  excellence  of  the  whole  structure.* 


*  This  bridge  ■was  considered,  at  the  time  it  was  built,  to  be  a 
yery  durable  and  scientific  structure  ;  but,  in  1S40,  it  was  found  to 
be  in  so  decayed  a  state  that  imnacdiato  repairs  were  necessary  to 
render  it  in  any  degree  safe  for  travel ;  a  thorough  examination  was 
made,  -which  resulted  in  a  recommendation  to  remove  the  clay  and 
stones  referred  to,  and  make  such  other  alterations  as  the  case  might 
demand. 

In  the  Bay  State  Democrat  of  October  8,  1842,  we  find  the  fol- 
lowing description  of  the  repairs  made  at  that  time  :  — 

"  Warren  Bridge  has  recently  been  thoroughly  repaired  in  all  its 
parts.  All  the  old  timbers  have  been  removed,  and  new  materials 
substituted.  This  -work  has  been  done  under  the  direct  superin- 
tendence of  Ebenezer  Barker,  Esq.,  the  agent  of  Warren  Bridge, 
■who  has  completed  it  in  a  manner  highly  creditable  to  himself,  and 
■worthy  of  the  magnitude  of  the  enterprise.  It  is  a  fine  specimen  of 
mechanical  skQl,  is  somewhat  novel  in  its  style  of  execution,  and 
may  be  looked  upon  as  one  of  the  greatest  ■works  of  its  kind  in  the 
country.  We  have  thought  that  some  statistics  in  connection  ■with 
this  subject  ■would  not  prove  uninteresting  to  the  general  reader. 

"  Warren  Bridge  ■was  incorporated  March  12,  1828,  and  opened  in 
the  subsequent  December.  It  is  now  1388  feet  in  length,  of  which 
1318  feet  are  covered  by  hexagonal  blocks  of  white  pine.  Its 
whole  width  is  44  feet  —  the  travel  way  being  30  feet,  and  the  side 
walks  occupying  7  feet  each.  To  begin  at  the  foundation  of  the 
work,  and  for  the  purpose  of  giving  the  pubUc  accurate  information 


TOWN'S  IMPROVED   BRIDGES. 

A  minute  and  accurate  description  of  Town's  i.n- 
provement  in  the  construction  of  wooden  and  iron 
bridges  is  given  in  a  succeeding  part  of  this  work. 
We  commend  the  article  to  the  learner,  as  being  par- 
ticularly worthy  of  his  serious  and  attentive  consid- 
eration. 


WHITE'S  TUBULAR  SUSPENSION   BRIDGE. 
[Patent  Right  secured.] 

Ammi  White,  Esq.,  of  Boston,  has  a  model  of  a 
bridge,  which  supersedes  the  necessity  of  piers  in 
crossing  our  largest  rivers.  He  asserts  that  it  can 
with  safety  be  extended,  even  for  railroad  purposes, 
fifteen  hundred  feet.  The  mode  of  its  construction 
is  as  follows  :  — 

"  First,  erect  the  towers  on  good  and  firm  abut- 
ments, or  on  a  rocky  bank  ;  then  extend  across  the 
stream  two  or  more  sets  of  stringers,  according  to  the 
number  of  road  beds  needed.  The  number  of  string- 
ers in  each  set  will  depend  upon  the  amount  of 
strength  required  in  the  bridge.  Each  stringer  is 
made  by  selecting  a  tree  of  proper  size,  which  is 
sawed  square,  and  is  tapered  from  the  top  to  within 
about  five  feet  of  the  base.  This  serves  as  a  start- 
ing-point, on  which  are  spliced  good  sound  boards, 
six  or  seven  inches  in  width,  on  a  curve  of  forty  feet 
in  five  hundred,  till  the  required  length  and  thickness 
is  obtained,  the  whole  terminating  in  a  corresponding 
timber  which  forms  the  other  extremity.  Li  securing 
one  board  upon  another,  care  is  taken  to  fix  keys  of 
wood  or  iron  into  mortises  made  half  into  one  board, 
and  half  into  the  other,  to  prevent  the  stringer  from 
elongating,  which,  with  the  additional  bolts  placed 
near  the  dowels,  is  as  incapable  of  divulsion  as  the 


of  its  whole  construction,  we  wiU  say,  first,  that  on  the  heads  of  the 
pUes  white  pine  caps,  14  inches  square,  are  placed  ;  on  these  caps 
rest  stringers  6  by  14  inches,  of  the  same  material,  in  a  longitudinal 
direction,  being  on  the  outside  12  inches  deep  ;  thus  making  in  the 
centre  a  crown  of  two  inches  elevation.  On  these  stringers,  trans- 
versely or  at  right  angles,  rest  yellow  N.  C.  pine  ribbons,  or  laths. 
4  by  5  inches,  and  spiked  to  every  other  stringer  by  8  uich  spikes. 
Upon  the  end  of  these  ribbons,  and  over  the  outside  stringer  of  the 
road  way,  white  pine  edge  timber,  10  by  Oj  inches,  is  laid  so  as  to 
project  2  inches  each  way  beyond  the  stringer  beneath  it.  This  tim- 
ber is  bolted  to  the  stringers  once  in  every  4  feet,  to  secure  more 
firmly  the  ends  of  the  ribbons  in  then-  places  ;  and  on  the  under  side 
of  these  timbers,  and  about  one  inch  from  each  edge,  grooves  of 
half  an  inch  deep  and  wide  are  made. 

"  On  such  a  foundation  as  this,  the  white  pine  blocks  —  which,  by 
the  way,  are  of  Maine  pine,  and  have  been  alluded  to  —  are  laid.  As 
a  matter  of  experiment,  blocks  of  10  and  11  inches  size  are  put 
down  on  the  Boston  side,  and  of  12  inch  size  on  the  Charlestown 
side.  These  blocks  are  all  tongued  and  grooved,  or  matched,  which 
serves  to  secure  the  ■(vhole  firmly  together,  and  to  present  an  even 
and  uniform  surface.  On  the  surface  of  these  blocks  is  put  a  liquid 
preparation  —  first,  a  coat  of  turpentine  mLxed  with  oil,  then  a  coat 
of  tar  and  pitch  poured  on  very  hot.  To  this  is  added  a  coat  of 
gravel,  rolled  in  by  a  machine,  so  as  to  fill  the  interstices  and  pores 
of  the  blocks.    The  object  of  all  this  care  is  to  preserve  the  material 


36 


INTRODUCTION. 


tree  itself.  This  suspension  cliain  or  stringer  is  run 
across  the  stream  by  means  of  a  wire  cable  and  pul- 
leys, and  when  locked  and  keyed  fast  in  the  towers, 
with  the  two  backstays,  is  allowed  to  take  a  catenary 
curve.  After  a  sufficient  number  has  been  extended 
across,  the  suspension  rods  are  bolted  to  them  and  to 
the  girders,  which  arc  made  slightly  arching,  and  to 
the  floor  joist.  The  rafter  is  connected  with  the 
stringer  and  top  of  the  suspension  rod,  to  which  is 
bolted  the  roof,  constructed  of  double  diagonal 
hoarding.  The  floor,  if  a  turnpike  bridge,  made  of 
double  diagonal  planking,  bolted  together,  is  then 
laid,  and,  in  the  capacity  of  cross  bracing,  serves  to 
render  firm  the  whole  structure.  If  a  railroad  bridge, 
the  cross  bracing  is  fitted  under  the  floor  joist,  in  con- 
nection with  the  girders.  By  loading  either  kind  of 
bridge  with  double  the  weight  it  is  required  to  sus- 
tain, the  girders  will  be  brought  down  to  a  level,  and, 
while  the  weight  is  on,  the  sides  are  covered  with  a 
double-diagonal  boarding,  similar  to  that  of  the  roof, 
both  of  which  must  be  firmly  attached  to  the  towers 
and  backstays  to  form  a  part  of  the  strength  of  the 


of  the  bridge,  to  make  it  water-tight,  and  to  prevent  horses  from 
slipping  in  travelling. 

"  We  would  say  here,  that  about  40  feet  of  the  bridge,  and  in  differ- 
ent sections  of  the  same,  are  laid  blocks  of  chestnut  wood,  from 
New  Hampshire. 

"  Under  the  sidewalks,  the  outside  stringer  is  12  inches  wide,  and 
the  inside  6  by  12.  On  these  are  placed  floor  joists,  3  by  5  inches, 
covered  by  two  inch  plank.  The  railing  is  handsome  and  perma- 
nent ;  and  near  the  draw  is  a  wooden  covering,  with  a  25  feet  roof, 
for  the  convenience  of  pedestrians  in  inclement  weather.  The  num- 
ber of  lamps  and  lamp  posts  arc  22.  The  form  of  the  bridge  is  a 
regular  ascending  plain,  rising  from  the  respective  abutments  to  the 
draw,  about  4  inches  to  every  100  feet." 

The  structure  remained  in  the  form  in  which  it  was  thus  repaired 
until  1846,  when  it  was  found  that  the  blocks  -with  which  the  sur- 
face was  covered  had  decayed  so  much  that  it  was  necessary  to 
remove  them,  and  it  was  at  length  decided  to  cover  the  southern 
pine  timbers,  before  referred  to,  with  common  two  inch  pine  planks, 
and  these  again  in  the  same  manner.  This  is  the  form  in  which  the 
surface  is  now  covered,  and  it  is,  without  doubt,  the  best  method 
which  has  been  made  use  of  since  the  bridge  was  first  built. 

How  long  the  blocks  would  have  lasted  under  an  ordinary  amount 
of  travel,  we  are  not  prepared  to  state  ;  but  it  was  foimd  that  the 
blocks  at  the  outer  edge  of  the  bridge  were  in  a  tolerable  state 
of  preservation,  while  those  in  the  centre  were  in  a  very  decayed 
state. 

It  may  be  well  here  to  state,  in  order  to  give  the  reader  some 
idea  of  the  trave  over  this  bridge,  that  from  an  account  kept  by 
order  of  Marshal  Tukey,  on  Saturday,  October  6,  1851,  from  half 


bridge.  The  direct  arches  are  formed  by  bolting  to- 
gether planks  on  the  right  curve.  One  springs  from 
the  abutment,  and  connects  with  the  stringer  at  the 
top  of  the  suspension  rod  ;  the  other  starts  from  the 
same  point,  and  connects  with  the  other  girder,  both 
connecting  in  their  course  with  the  suspension  rods. 
The  side  guards,  or  braces,  are  formed  by  fitting  a 
fender  rave  to  the  floor  joist,  which  extends  over  the 
girder  several  feet,  according  to  the  length  of  the 
bridge.  Short  rafters  connect  with  the  fender  rave 
and  the  suspension  rod.  These,  together  with  the 
projecting  floor  joists,  are  covered  with  double  diag- 
onal boarding.  These  braces  prevent  the  bridge 
from  vibrating.  The  backstays  connected  with  the 
studs  inserted  in  the  sills  of  the  towers  extend  back 
on  shore  the  required  distance,  and  are  firmly  at- 
tached to  stone  posts,  deeply  set  in  the  ground  at  the 
extremity  of  the  sills." 

[As  regards  the  strength,  economy,  durability, 
and  safety  of  this  bridge,  we  feel  warranted  in 
saying  it  excels  that  of  a  great  majority  of  bridges. 
—  Editors.] 

past  six,  A.  M.,  until  half  past  seven,  P.  M.,  as  published  in  the  Com- 
monwealth newspaper  at  the  time,  was  3158  vehicles,  6223  passen- 
gers in  the  same,  and  6095  passengers  on  foot.  In  consideration  of 
this  immense  amount  of  travel,  and  also  that  the  principal  part  of 
the  vehicles  consist  of  heavily-ladcd  trucks  and  large  freight  wag- 
ons, it  is  a  matter  of  astonishment  that  the  blocks  lasted  as  long  as 
they  did  ;  for,  as  may  be  supposed,  hollows  and  channels  were  soon 
formed  in  them,  and  the  water  standing  in  the  same  caused  a  con- 
stant decay. 

In  reference  to  this  kind  of  paving,  we  would  state,  for  the  benefit 
of  our  readers,  that  it  has  been  thoroughly  tested  in  the  streets  of 
Boston,  in  some  eases  using  hemlock,  and  in  some  others  spruce 
but  the  same  result  as  that  with  the  pine  on  the  bridge  has  followed 
and  that  now  rough  granite  blocks,  twelve  inches  square,  are  found 
to  be  the  most  serviceable  as  well  as  economical. 

We  ought  perhaps  to  state  in  regard  to  the  last  repairs  on  Warren 
Bridge  that,  at  the  Boston  end  about  the  Fitchburg  Depot,  the 
timbers  were  lowered  and  covered  with  mud  from  the  dock  for 
about  two  feet  deep,  and  upon  this,  in  the  centre  of  the  bridge,  as 
far  as  the  draw,  is  placed  granite  blocks,  as  above  described,  and 
that  the  sidewalks  for  the  same  distance  are  paved  with  bricks. 
This  method  seems  to  work  well,  as  yet,  and  it  has  been  so  highly 
approved  that  a  new  bridge  which  is  now  being  erected  on  a  new 
road  leading  from  the  Mill  Dam  Avenue  to  Brookline  is  constructed 
for  the  entire  length  in  the  same  manner. 

To  our  respected  friend,  Ebenezer  Barker,  Esq.,  who  is  superin- 
tending the  new  bridge,  we  tender  our  acknowledgments  for  his 
gentlemanly  and  kind  assistance  in  procuring  the  facts  relative  to 
this  importimt  structure  —  the  Warren  Bridge.  —  Editors. 


ill 


vV  H 


M 


H 


//r.rifr/^i//  . 


f'r/rlf/f>»  . 


CIVIL    ARCHITECTURE. 


PRACTICAL    QEOMETEY, 


The  System  of  Geometry  here  introduced  is  as  concise  and  sim- 
ple as  is  compatible  with  a  proper  understanding  of  this  interesting 
branch  of  mechanical  science. 

Descriptive  Geometry  is  employed  to  communicate  a  knowledge 
of  different  objects.  It  furnishes  the  means  of  constructing  ge- 
ographical charts,  plans  of  buildings  and  machines,  architectural 
designs,  sun  dials,  &c.  It  is  used,  likewise,  to  describe  the  forms 
and  relative  positions  of  objects.  By  it,  stone  cutters,  carpenters, 
shipbuilders,  &c.,  find  the  dimensions  of  the  works  which  they  ex- 
ecute, inasmuch  as  these  dimensions  admit  of  a  rigorous  definition. 

That  a  knowledge  of  Geometry  is  essential  to  the  greater  part  of 
our  practical  mechanics,  does  not  admit  of  a  doubt ;  yet  they  have 
too  generally  regarded  the  subject  with  a  degree  of  indifference,  as 
though  the  ends  proposed  to  be  accomplished  by  it  could  be  as 
accurately,  and  much  more  easily,  attained  by  other  means.  This 
erroneous  notion,  however,  is  fast  giving  way  to  the  force  of  truth 
and  demonstration  ;  and  perhaps  more  attention  is  paid  to  the  sub- 
ject at  the  present  time,  by  operative  mechanics,  than  at  any  pre- 
vious period  since  the  discovery  of  the  science.  Many  attempts 
have  been  made  to  simplify  the  study,  and  to  render  the  acquisition 
of  it  more  easy  to  the  learner.  In  many  instances,  these  attempts 
have  been  partially  successful ;  but  the  student  will  bear  in  mind 
the  memorable  reply  of  Euclid  —  "  Tliere  is  no  royal  road  to  geom- 
etry." There  is  no  turnpike,  though  there  are  some  cross  roads  ; 
but  we  doubt  not  that  he  who  travels  the  old  road,  which  has  been 
so  often  proved  to  be  good,  and  over  which  so  many  have  travelled 
before  him,  will  be  as  well  pleased  with  his  journey  when  it  is 
accomplished  as  he  who  arrives  at  the  end  by  a  shorter  route.  It 
has  been  said,  but  we  trust  with  more  severity  than  truth,  that  the 
generality  of  mechanics  are  displeased  at  the  sight  of  a  geometrical 
theorem.  If  so,  a  very  little  attention  to  the  subject  will  satisfy 
them  that  no  study  can  be  better  calculated  to  awaken  the  dormant 
faculties  of  the  mind  and  to  force  them  into  action. 


DEFINITIONS. 
Plate  1. 

1.  Geometry  is  that  science  which  treats  of  the 
descriptions  and  properties  of  magnitudes  in  general. 

2.  A  point  has  neither  parts  nor  magnitude,  as  A. 


3.  A  line  is  length,  without  breadth  or  thickness, 
asB. 

4.  Superficies  has  length  and  breadth  only. 

5.  A  solid  is  a  figure  of  three  dimensions,  having 
length,  breadth,  and  thickness.  Hence,  surfaces  are 
the  extremities  of  solids,  and  lines  the  extremities  of 
surfaces,  and  points  the  extremities  of  Unes. 

6.  Lines  are  either  right,  curved,  or  mixed,  as  E. 

7.  A  right  or  straight  line  lies  in  the  same  direc- 
tion between  its  extremities,  and  is  the  shortest  dis- 
tance between  two  points. 

8.  A  curve  continually  changes  its  directions  be- 
tween its  extreme  points,  as  F. 

9.  Lines  are  either  parallel,  oblique,  perpendicular, 
or  tangential. 

10.  Parallel  lines  are  always  at  the  same  distance, 
and  will  never  meet,  though  ever  so  far  produced,  as 
C  and  D. 

11.  Oblique  right  lines  in  the  same  plane  change 
their  distance,  and  would  meet,  if  produced,  as  I. 

12.  One  line  is  perpendicular  to  another  when  it 
inclines  no  more  to  one  side  than  another,  as  H. 

13.  One  line  is  tangent  to  another  when  it  touches 
it  without  cutting,  when  both  are  produced,  as  G. 

14.  An  angle  is  the  inclination  of  two  lines  to- 
wards one  another,  meeting  in  a  point,  as  J. 

15.  Angles  are  either  right,  acute,  or  oblique,  as  K. 

16.  A  right  angle  is  that  which  is  made  by  one 
line  perpendicular  to  another,  or  when  the  angles  on 
each  side  are  equal,  as  M. 

17.  An  acute  angle  is  less  than  a  right  angle,  as 
N,2. 

18.  An  obtuse  angle  is  greater  than  a  right  angle, 
as  N. 


38 


PRACTICAL    GEOMETRY. 


19.  Superficies  are  either  plane  or  curved. 

20.  A  plane,  or  plane  surface,  is  that  to  which  a 
right  line  will  every  way  coincide  ;  but  if  not,  it  is 
curved. 

21.  Plane  figures  are  bounded  either  by  right  lines 
or  curves. 

22.  Plane  figures,  bounded  by  right  lines,  haije 
names  according  to  the  number  of  their  sides  or 
angles,  for  they  have  as  many  sides  as  angles.  The 
least  number  is  three. 

23.  An  equilateral  triangle  is  that  whose  three 
sides  are  equal,  as  O. 

24.  An  isosceles  triangle  has  only  two  sides  equal, 
as  P. 

25.  A  scalene  triangle  has  all  its  sides  unequal,  as 
Qor  U. 

26.  A  right  angled  triangle  has  one  right  angle,  as 
R. 

27.  Other  triangles  are  oblique  angled,  and  are 
either  obtuse  or  acute. 

28.  An  acute  angled  triangle  has  all  its  angles 
acute,  as  S  or  T. 

29.  An  obtuse  angled  triangle  has  one  obtuse 
angle,  as  U. 

30.  A  figure  of  four  sides  and  angles  is  called  a 
quadrangle,  or  quadrilateral,  as  V,  W,  X,  Y,  Z,  &. 

31.  A.  parallelogram  is  a  quadi'Uateral,  which  has 
both  pairs  of  its  opposite  sides  parallel,  as  V,  W,  X, 
Y,  and  takes  the  following  particular  names  :  — 

32.  A  rectangle  is  a  parallelogram,  having  all  its 
mgles  right  ones,  as  V  and  W. 

33.  A  square  is  an  equilateral  rectangle,  having  all 
its  sides  equal,  and  aU  its  angles  right  ones,  as  W. 

34.  A  rhombus  is  an  equilateral  parallelogram, 
whose  angles  are  oblique,  as  X. 

35.  A  rhomboid  is  an  oblique-angled  parallelogram, 
as  Y 

36.  A  trapezium  is  a  quadrilateral,  which  has 
neither  pair  of  its  sides  parallel,  as  Z. 

37.  A  trapezoid  has  only  one  pair  of  its  opposite 
sides  parallel,  as  &. 

38.  Plane  figures  having  more  than  four  sides  are, 
in  general,  called  polygons,  and  receive  other  partic- 
ular names,  according  to  the  number  of  their  sides 
or  angles. 

39.  A.  pentagon  is  a  polygon  of  five  sides.  A  hex- 
agon has  six   sides,  a  heptagon  seven,  an  octagon 


eight,  a  nonagon  nine,  a  decagon  ten,  an  undecagon 
eleven,  and  a  dodecagon  twelve  sides. 

40.  A  regular  polygon  has  all  its  sides  and  angles 
equal ;  and  if  they  are  not  equal,  the  polygon  is 
irregular. 

41.  Aji  equilateral  triangle  is  also  a  regular  figure 
of  three  sides,  and  a  square  is  one  of  four  —  the 
former  being  called  a  trigon,  and  the  latter  a  tetra- 
gon. 

Plate  2. 

42.  A  circle  is  a  plane  figure  bounded  by  a  curve 
line,  called  the  circumference,  which  is  every  where 
equidistant  from  a  certain  point  within,  called  its 
centre. 

43.  The  radius  of  a  circle  is  a  right  line  drawn 
from  the  centre  to  the  circumference,  a  b,  at  A. 

44.  A  diameter  of  a  circle  is  a  right  line  drawn 
through  the  centre,  terminating  on  both  sides  of  the 
circumference,  as  c  d,  at  B. 

45.  An  arc  of  a  circle  is  any  part  of  the  circum- 
ference, 

46.  A  chord  is  a  right  line  joining  the  extremities 
of  an  arc,  as  a  b,  at  C. 

47.  A  segment  is  any  part  of  a  circle  bounded  by 
an  arc  and  its  chord,  as  D. 

48.  A  semicircle  is  half  the  circle,  or  a  segment 
cut  off  by  the  diameter,  as  E. 

49.  A  sector  is  any  part  of  a  circle  bounded  by  an 
arc  and  two  radii,  drawn  to  its  extremities,  as  F. 

50.  A  quadrant,  or  quarter  of  a  circle,  is  a  sector, 
having  a  quarter  of  the  circumference  for  its  arc,  and 
the  two  radii  are  perpendicular  to  each  other,  as  G. 

51.  The  height  or  altitude  of  any  figure  is  a  per- 
pendicular let  fall  from  an  angle,  or  its  vertex,  to  the 
opposite  side,  called  the  base,  as  a  b,  at  H. 

52.  When  an  angle  is  denoted  by  three  letters,  the 
middle  one  is  the  place  of  the  angle,  and  the  other 
two  denote  the  sides  containing  that  angle.  Thus  : 
let  a  &  c  be  the  angle  at  I,  then  b  will  be  the  angular 
point,  and  a  b  and  b  c  will  be  the  two  sides  contain- 
ing that  angle. 

53.  The  measure  of  any  right-lined  angle  is  an 
arc  of  any  circle  contained  between  the  two  lines 
which  form  the  angle,  the  angular  point  being  in  the 
centre,  as  K.  Thus,  if  the  arc  b  c  d  he  double  of  the 
arc  b  c,  then  the  angle  bad  will  be  double  that  of 
b  a  c. 


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li 

PRACTICAL    GEOMETRY. 


39 


PROBLEMS. 


Plate  3. 


PROBLEM  :. 

To  bisect  a  given  line,  A  B. 

1.  From  the  points  A  and  B,  as  centres,  with  any 
distance  greater  than  half  A  B,  describe  arcs  cutting 
each  other  in  c  and  d. 

2.  Draw  the  line  c  d,  and  the  point  E,  where  it  cuts 
A  B,  will  be  the  middle  of  the  line  required. 

PEOBLEM  II. 

From  a  given  point,  C,  in  a  given  right  line, 
A  B,  to  erect  a  perpendicular. 

Fig.  1.   Wlien  the  point  is  near  the  middle  of  the  line. 

1.  On  each  side  of  the  point  C  take  any  two  equal 
distances,  C  d  and  C  e. 

2.  From  d  and  e,  with  any  radius  greater  than  C  d, 
or  C  e,  describe  two  arcs  cutting  each  other  in  /. 

3.  Through  the  points/  C  ,  draw  the  line/  C,  and 
it  will  be  the  perpendicular  required. 

Fig.  2.   When  the  point  is  at,  or  near,  the  end  of  the  line. 

1.  Take  any  point  d  above  the  line,  and  with  the 
radius  or  distance,  d  C,  describe  the  arc  e  C/,  cutting 
A  B  in  e  and  C. 

2.  Through  the  centre  d  in  the  point  e,  draw  the 
line  e  df,  cutting  the  arc  e  Cf,  inf. 

3.  Through  the  points  /  C  draw  the  line  /  C,  and 
it  will  be  the  perpendicular  required. 

PROBLEM  III. 

From  a  given  point,  C,  out  of  a  given  right  line, 
A  B,  to  let  fall  a  perpendicular. 

1.  From  the  point  C,  with  any  radius,  describe  the 
arc  d  e,  cutting  A  B  in  e  and  d. 

2.  From  the  points  e  d  with  the  same,  or  any  other 
radius,  describe  two  arcs  cutting  each  other  in  /. 

3.  Through  the  pomts  C  /  di-aw  the  line  CD/, 
and  C  D  will  be  the  perpendicular  required. 

PROBLEM  IV. 

A  t  a  given  point,  D,  upon  the  right  line,  D  E,  to 
make  an  angle  equal  to  a  given  angle,  a  B  J. 

1.  From  the  point  B,  with  any  radius,  describe  the 
arc  a  b,  cutting  the  legs  B  a,  B  6,  in  the  points  a  and  b. 


2.  Draw  the  line  D  e,  and  from  the  point  D,  with 
the  same  radius  as  before,  describe  the  arc  ef,  cutting 
DEin  e. 

3.  Take  the  distance  b  a,  and  apply  it  to  the  arc 
ef,  from  e  to/. 

4.  Through  the  points  D/draw  the  line  D/,  and 
the  angle  e  D/will  be  equal  to  the  angle  6  B  a,  as 
was  required. 

PROBLEM  V. 

To  divide  a  given  angle,  ABC,  into  two  equal 

angles. 

1.  From  the  point  B,  with  any  radius,  describe  the 
arc  A  C. 

2.  From  A  and  C,  with  the  same  or  any  other  ra- 
dius, describe  arcs  cutting  each  other  in  d. 

3.  Draw  the  line  B  d,  and  it  will  bisect  the  angle 
A  B  C,  as  was  required. 

PROBLEM  VI. 

To  trisect  or  divide  a  right  angle,  ABC,  into 
three  equal  angles. 

1.  From  the  point  B,  with  any  radius  B  A,  describe 
the  arc  A  C,  cutting  the  legs  B  A  and  B  C,  in  A 
and  C. 

2.  From  the  point  A  and  C,  with  the  radius  A  B, 
or  B  C,  cross  the  arc  A  C,  in  (?  and  e. 

3.  Through  the  points  e  d  draw  the  lines  B  e,  B  rf, 
and  they  will  trisect  the  angle,  as  was  required. 

PROBLEM  VII. 

Through  a  given  point,  C,  to  draw  a  line  par- 
allel to  a  given  line,  A  B. 

1.  Take  any  point  rf,  in  A  B,  upon  d  and  C,  with 
the  distance  C  d,  describe  two  arcs,  e  C  and  d  f,  cut- 
ting the  line  A  B,  in  e  and  d. 

2.  Make  d  f  equal  to  e  C ;  through  C  and  /  draw 
C/,  which  will  be  the  line  required. 

Fig.  2.  Wlien  the  parallel  is  to  be  at  a  given  distance, 
C  D  from  A  B. 

1.  From  any  two  points  c  and  d,  in  the  line  A  B, 
with  a  radius  equal  to  C  D,  describe  the  arcs  e  and/. 

2.  Draw  the  line  C  B,  to  touch  those  arcs  without 
cutting  them,  and  it  will  be  parallel  to  A  B,  as  was 
required. 


40 


PRACTICAL    GEOMETRY. 


PROBLEM  VUI. 

To  divide  a  given  line,  A  B,  into  any  proposed 
number  of  equal  parts. 

1.  From  A,  one  end  of  the  line,  draw  A  c,  making 
any  angle  with  A  B ;  and  from  B,  the  other  end, 
draw  B  d,  making  the  angle  AB  d  equal  to  B  A  c. 

2.  In  each  of  the  lines  A  c,  and  B  d,  beginning  at 
A  and  B,  set  off  as  many  equal  parts,  of  any  length, 
as  A  B  is  to  be  divided  into. 

3.  Join  the  points  A  5,  1  4,  2  3,  &c.,  and  A  B  will 
be  divided  as  was  required. 

PROBLEM  IX. 

To  find  the  centre  of  a  given  circle,  or  one  al- 
ready described. 

1.  Draw  any  chord  A  B,  and  bisect  it  with  the 
perpendicular  C  D. 

2.  Bisect  C  D  with  the  diameter  E  /,  and  the  inter- 
section O  will  be  the  centre  required. 

PROBLEM  X. 

To  draw  a  tangent  to  a  given  cii-cle,  that  shall 
pass  through  a  given  point,  A. 

1.  From  the  centre  O,  draw  the  radius  O  A. 

2.  Tluough  the  point  A  draw  D  E  perpendicular 
to  O  A,  and  it  will  be  the  tangent  required. 

PROBLEM  XI. 

To  draw  a  tangent  to  a  circle,  or  any  segment 
of  a  circle,  ABC,  through  a  given  point,  B, 
without  making  use  of  the  centre  of  the 
circle. 

1.  Take  any  two  equal  divisions  upon  the  circle ; 
from  the  given  point  B,  towards  d  and  e,  draw  the 
chord  e  B. 

2.  Upon  B,  as  a  centre,  with  the  distance  B  d,  de- 
scribe the  arc  fd g,  cutting  the  chord  e  B,  in/. 

3.  Make  d  g  equal  to  df,  through  g  draw  g  B,  and 
it  wU".  be  the  tangent  required. 

PROBLEM  XII. 

A  circle,  A  B  C,  being  given,  and  a  tangent,  D 
H,  to  that  circle,  to  find  the  point  of  contact. 

1.  Take  any  point  e,  in  the  tangent  D  H ;  from  e, 
to  the  centre  of  the  circle  G,  draw  e  G. 


2.  Bisect  e  G,  in/,  and  with  the  radius /e,  or/  G, 
describe  the  semicircle  e  C  G,  cutting  the  tangent 
and  the  circle  in  C  ;  it  will  be  the  point  required. 


PROBLEM  XIII. 

Given  three  points,  ABC,  not  in  a  straight 
line,  to  find  a  number  of  points  Ipng  between 
them,  so  that  they  shaU  aU  be  in  the  circum- 
ference of  a  circle,  without  drawing  any  part 
of  the  circle,  or  finding  the  centre. 

1.  From  A,  through  B  and  C,  draw  A  B  and  A  /. 

2.  On  A,  as  a  centre,  with  any  radius  A/,  describe 
an  arc/e  d,  cutting  A  B  in  </,  and  A  C  mf. 

3.  Bisect  arc  df  in  e;  through  e  draw  A  e  h. 

4.  Join  C  B,  bisect  it  in  g,  draw  g  h  perpendicular, 
cutting  A  e  /t  at  A,  then  h  will  also  be  in  the  same 
circumference  with  A  C  B.  In  the  same  manner 
may  a  point  be  found  between  C  A  and  h  B. 

PROBLEM  XIV. 

Given  three  points,  ABC,  not  in  a  right  line, 
to  find  another  point  without  these  points,  so 
that  the  four  points  shall  all  be  in  the  circum- 
ference of  a  circle,  without  drawing  any  part 
of  the  circle,  or  finding  the  centre. 

1.  Draw  A  e  and  A  C,  from  A,  through  B  and  C. 

2.  On  A,  as  a  centre,  with  any  radius  A  e,  draw 
the  arc  e/g-,  cutting  A  B  in  e,  and  A  C  in/. 

3.  Make  f  g  equal  to  /  e,  through  A  and  g  draw 
A  g  indefinitely  towards  d. 

4.  Upon  C,  with  the  distance  C  B,  cross  the  line 
Ag  &i  d;  it  wiU  be  the  point  required. 

If  a  fifth  point,  or  any  other  number  of  points,  are 
required,  the  process  will  be  the  same. 

Plate  3. 

PROBLEM  XV. 

Given  three  points,  ABC,  not  in  a  straight  line, 
to  draw  a  circle  through  them. 

1.  Bisect  the  lines  A  B  and  B  C  by  the  perpen- 
diculars, meeting  at  d. 

2.  Upon  d,  with  the  distance  d  A,  dB,  ox  d  C,  de- 
scribe A  B  C ;  it  will  be  the  circle  required. 


W  II 


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XXV. 


XXVI 


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41 


PROBLEM    XVI. 

To   describe  the  segment    of    a    circle   to    any 
length,  A  B,  and  breadtli,  C  D. 

1.  Bisect  A  B,  by  (lie  perpendicular  D  g;  cutting 
A  B  in  C. 

2.  From  r,  make  c  D  on  the  perpendicular  equal 
to  C  D. 

3.  Bisect  A  D,  by  a  perpendicular  e  f,  cutting  D  g 

ill  S'- 

4.  Upon  g-,  the  centre,  describe  A  D  B ;  it  will  be 
the  segment  required. 

PROBLEM   XVII. 

To  describe  the  segment  of  a  circle,  by  means 
of  two  rules,  to  any  length,  A  B,  and  per- 
pendicular height,  C  D,  in  the  middle  of  A 
B,  without  making  use  of  the  centre. 

It  will  be  most  convenient  for  practice  to  make  the 
rules  C  E  and  C  F  each  equal  to  A  B,  as  room  is 
sometimes  wanted. 

1.  Place  the  rules  to  the  height  at  C,  bring  the 
edges  close  to  A  and  B,  tack  them  together  at  C,  and 
fix  a  rod  across  to  keep  them  tight. 

2.  Put  in  pins  at  A  and  B,  then  move  your  rules 
round  these  pins  ;  hold  a  pencil  to  the  angular  point 
at  C ;  it  will  describe  the  segment  required. 

Fig.  2.      Bi/  means  of  a  triangle. 

Let  A  B  be  the  length  of  the  segment,  and  C  D 
the  perpendicular  height  in  the  middle. 

1.  Through  the  points  D  and  B  draw  D  B. 

2.  Draw  D  E  parallel  to  A  B  for  conveniency  • 
make  D  E  equal  to  D  B,  and  join  E  B. 

3.  Make  a  triangle  E  D  B ;  put  in  pins  at  the 
points  A  D  B ;  then  move  your  triangle  round  the 
points  D  and  B,  and  the  angular  point  will  describe 
half  the  segment;  the  other  half  will  be  described  in 
the  same  manner,  which  will  complete  the  whole 
segment,  as  was  required. 

Fig.  3-     Another  method,  by  means  of  points. 

Let  A  B  be  the  length,  and  C  D,  bisecting  A  B, 
the  perpendicular  height. 

1.  Through  D,  draw  G  H  parallel  to  A  B. 

2.  Draw  D  B,  the  half  chord. 

3.  From  B,  make  B  H  perpendicular  to  D  B,  cut- 
ting G  H  in  H,  and  make  D  G  equal  to  D  H. 

6 


4.  Draw  A  F  and  B  E,  each  perpendicular  to  A  B, 
cutting  G  H  in  F  and  E. 

5.  Divide  D  G,  D  H,  C  A,  C  B,  and  A  F,  B  E, 
each  into  a  like  number  of  equal  parts,  as  five. 

G.  Draw  the  cross  lines,  4  4,  3  3,  2  2,  11,  &e. 

7.  From  the  division  on  A  F,  and  B  E,  draw 
lines  to  D,  cutting  the  other  cross  lines  at  d,  e, 
/.  §•)  &c. 

8.  Put  pins  in  these  points,  bend  a  sbp  round  them, 
and  draw  the  curve  by  it,  which  will  be  the  segment 
reqiiired. 

Fig.  4.     Another  method,  by  points  nearly  true,  when 
the  segment  is  very  flat. 

Let  A  B  be  the  length,  and  C  D,  bisecting  A  B, 
the  perpendicular  height. 

1.  Draw  A  E  and  B  F,  perpendicular  to  A  B,  each 
equal  to  C  D. 

2.  Divide  C  B  and  C  A  each  into  the  same  num- 
ber of  equal  parts,  as  five. 

3.  From  the  points  4,  3,  2,  1,  &c.,  on  A  B,  draw 
the  perpendicular  4  4,  3  3,  2  2, 11,  &c.,  to  A  B. 

4.  Divide  A  E  and  B  F  into  five  equal  parts 
each. 

5.  Draw  lines  from  the  points  1,  2,  3,  4,  5,  at  each 
end,  to  D,  and  complete  the  segment  in  the  same 
manner  as  fig.  3. 

PROBLEM  XVIII. 

To  describe  a  circle  within  a  given  triangle,  so 
that  ABC  will  be  tangical. 

1.  Take  equal  distances  on  C  A,  also  on  C  B, 
from  C ;  intersect  towards  D. 

2.  Draw  lines  E  D,  from  A  and  C,  through  the 
intersection  E  and  D ;  from  E  let  fall  a  perpendicu- 
lar, which  will  be  the  radius  of  the  circle  required. 

PROBLEM  XIX. 

In  a  given  square,  A  B  C  D,  to  inscribe  a  reg- 
ular octagon. 

1.  Draw  the  diagonals  A  C  and  B  D,  intersect- 
ing at  e. 

2.  Upon  the  points  A  B  C  D,  as  centres,  with  a 
radius  e  C,  describe  arcs  h  e  l,ke  n,  meg,fe  i. 

3.  Jomfn,mh,ki,lg;  it  will  be  the  octagon  re- 
quired. 


42 


PRACTICAL    GEOMETRY. 


PROBLEM  XX. 

In  a  given  circle  to  inscribe  an  equilateral  tri- 
angle, a  hexagon,  or  a  dodecagon. 

For  the  Equilateral  Triangle. 

1.  Upon  any  point  A,  in  the  circumference,  with 
the  radius  A  G,  describe  the  arc  B  G  F. 

2.  Draw  B  F,  make  B  D  equal  to  B  F. 

3.  Join  D  F,  and  B  D  F  will  be  the  equilateral 
triangle  required. 

For  the  Hexagon. 
Carry  the  radius  A  G  sLx  times  round  the  circum- 
ference ;  the  figure  A  B  C  D  E  F  will  be  the  hexagon. 

For  the  Dodecagon. 

Bisect  the  arc  A  B  in  //,  and  A  h  being  carried 
twelve  times  round  the  chrcumference,  will  also  form 
the  dodecagon. 

PROBLEM  xxr. 

In  a  given   circle  to  inscribe  a   square   or  an 
octagon. 

1.  Draw  the  diameters  A  C  and  B  D  at  right 
angles. 

2.  Join  A  B,  B  C,  C  D,  D  A,  and  A  B  C  D  will 
be  the  square. 

For  the  Octagon. 

Bisect  the  arc  A  B  in  E,  and  A  E  being  carried 
eight  times  round,  will  also  form  the  octagon. 


PROBLEM  XXII. 

In  a  given   circle  to  inscribe  a  pentagon  or  a 
decagon. 

For  a  Pentagon. 

1.  Draw  the  diameters  A  C  and  B  D  at  right 
angles. 

2.  Bisect  B  C  in  /,  upon  /;  Avith  the  distance/ D 
describe  the  arc  D  g  upon  D ;  with  the  distance  D  g 
describe  the  arc  g  H,  cutting  the  circle  in  H. 

3.  Join  D  IT,  and  caiTy  it  round  the  circle  five  times, 
which  wUl  form  the  pentagon. 

For  the  Decagon. 

Bisect  the  arc  D  II  in  i,  and  D  i  being  carried  ten 
times  round,  will  also  form  the  decagon. 


PROBLEM   XXIII. 

In    a    given    circle    to    inscribe    any    regulai 
polygon. 

1.  Draw  tlic  diameter  A  B,  from  E  the  centre ;  erect 
Ihc  perpendicular  E  F  C,  cutting  the  circle  at  F. 

2.  Divide  E  F  into  fom-  equal  parts,  and  set  three 
parts  from  F  to  C. 

3.  Divide  the  diameter  A  B  into  as  many  equal 
parts  as  the  polygon  is  requu'ed  to  have  sides. 

4.  From  C,  through  the  second  division  in  the  di- 
ameter, draw  C  D. 

5.  Join  A  D  ;  it  will  be  the  side  of  the  polygon 
rcquu'ed. 

PROBLEM  XXIV. 

Upon  a  given  line,  A  B,  to  describe  an  equilat- 
eral triangle. 

1.  Upon  the  points  A  and  B,  with  a  radius  equal 
to  A  B,  describe  arcs  cutting  each  other  at  C. 

2.  Draw  A  C  and  B  C;  it  will  be  the  triangle 
required. 

PROBLEM  XXY. 

Upon  a  given  line,  A  B,  to  describe  a  square. 

1.  Upon  A  and  B,  as  centres,  with  a  radius  A  B, 
describe  two  arcs,  A  e  C,  B  e  D,  cutting  each  other 
at  e. 

2.  Bisect  A  e  at/;  from  e  make  e  D  and  e  C  equal 
to  ef. 

3.  Join  A  D,  D  C,  C  B,  and  it  will  be  the  square 
required. 

PROBLEM  XXVI. 

Upon  a  given  line,  A  B,  to  construct  any  regular 
polygon. 

1.  Upon  A  and  B,  as  centres,  with  a  radius  A  B, 
describe  two  arcs  intersecting  each  other  at  F. 

2.  From  B,  draw  B  C  perpendicular,  and  divide 
the  arc  A  C  into  as  many  equal  parts  as  the  polygon 
is  to  have  sides. 

3.  Through  the  second  division  D  draw  B  G,  make 
F  E  equal  to  F  D,  and  through  E  draw  A  G,  meet- 
ing B  G  at  G ;  then  G  will  be  the  centre,  and  G  A 
the  radius  of  a  circle,  that  will  contain  A  B  to  any 
number  of  sides  required. 

PROBLEM  XXVII. 

To  make  a  triangle,  whose  three  sides  shall  be 


PI .  I 


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X  \  1 X 


XXX. 


I'  I         K       I,    n 


leF^Ovtti-v  Sc. 


PRACTICAL     GEOMETRY. 


43 


equal  to  three  given   lines,  D,  E,  F,  if  any 
two  are  greater  tlian  the  third. 

1.  Draw  A  B  equal  to  the  line  D. 

2.  Upon  B,  with  the  length  of  E,  describe  an  arc 
at  C. 

2.  Upon  B,  with  the  length  F,  describe  another  arc, 
intersecting  the  former  at  C. 

4.  Draw  A  C  and  C  B,  and  A  B  C  will  be  the  tri- 
angle required. 

Plate  4. 

PROBLEM   XXVIII. 

To  make  a  trapezium  equal  and   similar  to  a 
given  trapezium,  A  B  C  D. 

1.  Divide  the  given  trapezium  A  B  C  D  into  two 
triangles,  by  a  diagonal,  A  C. 

2.  ]Make  E  F  equal  to  A  B  upon  E  F,  construct 
the  triangle  E  F,  whose  three  sides  will  be  respec- 
tively equal  to  the  triangle  ABC. 

3.  Upon  E  G,  which  is  equal  to  A  C,  construct 
the  triangle  E  G  H,  w"hose  two  sides,  E  H  and  G  H, 
are  respectively  equal  to  A  D  and  C  D,  then  E  F 
G  H  wUl  be  the  trapezium  required. 

Li  the  same  manner  may  any  irregular  polygon  be 
made  equal  and  similar  to  a  given  irregular  polygon, 
by  dividing  the  given  polygon  into  triangles,  and  con- 
structing the  triangles  in  the  same  manner  in  the  re- 
quired polygon,  as  is  shown  by  figures. 

PROBLEM   XXIX. 

To  make  a  triangle  equal  to  a  given  trapezium, 
ABCD. 

1.  Draw  the  diagonal  B  D,  make  C  E  parallel  to 
to  it,  meeting  the  side  A  B,  produced  in  E. 

2.  Join  D  E,  and  A  D  E  will  be  the  triangle. 

PROBLEM  XXX. 

To  make  a  triangle  equal  to  a  given  right-lined 
figure,  ABODE.' 

1.  Produce  the  side  A  B  both  ways  at  pleasure. 

2.  Draw  the  diagonals  A  D  and  B  D,  and  make 
E  F  and  G  H  parallel  to  them. 

3.  Join  D  F,  D  G,  then  D  F  G  will  be  the  triangle 
required. 

Much  after  the  same  manner  may  any  other  right- 
lined  figure  be  reduced  to  a  triangle. 


PROBLEM  XXXI. 

To  reduce  a  triangle,  A  B  C,  to  a  rectangle. 

1.  Bisect  the  altitude  C  G,  in  D ;  tlu'ough  D  draw 
E  F  parallel  to  A  B. 

2.  From  B  draw  B  F  perpendicular  to  A  B,  through 
A  draw  A  E  parallel  to  B  F,  then  A  B  F  E  \vill  be 
the  rectangle  required. 

PROBLEM  XXXII. 

To  make  a  rectangle,  having  a  side  equal  to  a 
given  line,  A  B,  and  equal  to  a  given  rectan- 
gle, C  D  E  F. 

1.  Produce  the  sides  of  the  rectangle  C  F,  D  E, 
F  E,  and  CD. 

2.  Make  E  G  equal  to  A  B,  through  G  draw  L  H 
parallel  to  F  E,  cutting  C  F  produced  at  L. 

3.  Draw  the  diagonal  L  E,  and  produce  it  till  it 
cut  C  D  at  K. 

4.  Draw  K  H  paraUel  to  E  G,  then  wiU  E  I  H  G 
be  the  rectangle  required. 

PROBLEM  XXXIII. 

To  make  a  square  equal  to  a  given  rectangle, 
ABCD. 

1.  Produce  the  side  A  B,  make  B  E  equal  to  B  C. 

2.  Bisect  A  E,  in  I ;  on  I,  as  the  centre,  with  the 
radius  I  E  or  I  A,  describe  the  semicircle  A  H  E. 

3.  Produce  the  side  of  C  B  to  cut  the  circle  in  H; 
on  B  H  describe  the  square  B  H  G  F ;  it  will  be  the 
square  required. 

PROBLEM  XXXIV. 

To  make  a  square  equal  to  two  given  squares, 
A  and  B. 

1.  Make  D  E  equal  to  the  side  of  the  square  A, 
and  D  F  perpendicular  to  D  E,  equal  to  the  side  of 
the  square  B. 

2.  Draw  the  hypothenuse  F  E ;  on  it  describe  the 
square  E  F  G  H  ;  it  wiU  be  the  square  required. 

PROBLEM  XXXV. 

To  make  a  square  equal  to  three  given  squares, 
ABC. 

1.  Make  D  E  equal  to  the  side  of  the  square  A, 
and  D  F  perpendicular  to  D  E,  equal  to  the  side  of 
the  square  B. 

2.  Join  F  E ;  draw  F  G  perpendicular  to  it. 


44 


PRACTICAL     GEOMETRY 


3.  Make  F  G  equal  to  the  side  of  the  square  C ; 
join  G  E,  then  G  E  will  be  the  side  of  the  square 
required. 

PROBLEM   XXXVI. 

Two  right  lines,  A  B,  and  C  D,  being  given,  to 
find  a  third  proportional. 

1.  Make  an  angle  H  E  I  at  pleasure,  irom  E,  make 
E  F  equal  to  A  B,  and  E  G  equal  to  C  B ;  join  F  G. 

2.  Make  E  H  equal  to  E  G,  and  draw  H  I  parallel 
to  E  G,  then  E  I  will  be  the  third  proportional  re- 
quired, that  is,  E  F  :  E  G  : :  E  H  :  E  I,  or  A  B  : 
C  D  :  :  C  D  :  E  I. 

PROBLEM  XXXVII. 

Three  right  lines,  A  B,  C  D,  E  F,  being  given, 
to  find  a  fourth  proportional. 

1.  ]\Iake  the  angle,  H  G  I,  at  pleasure ;  from  G 
make  G  H  equal  to  A  B ;  G  I  equal  to  C  D ;  and 
join  H  I. 

2.  Make  G  K  equal  to  E  F,  draw  K  L  through  K 
parallel  to  H  I,  then  G  L  will  be  the  fourth  propor- 
tional required ;  that  is,  G  H  :  G  I :  :  G  K  :  G  L,  or 
A  B  :  C  D  : :  E  F  :  G  L. 

PROBLEM  XXXVIII. 

To  divide  a  given  line,  A  B,  in  the  same  propor- 
tion as  another,  C  D,  is  divided. 

1.  Make  any  angle  K  H  I,  and  make  H  I  equal 
to  A  B ;  then  apply  the  several  divisions  of  C  D  from 
H  to  K,  and  join  K  I. 

2.  Draw  the  lines  h  e,  i  f,  k  g,  parallel  to  I  K,  and 
the  line  H  I  will  be  divided  in  /;,  i,  k,  as  was  required. 

PROBLEM  XXXIX. 

Between  two  given  right  lines,  A  B,  and  C  D, 
to  find  a  mean  proportional. 

1.  Draw  the  right  line  E  G,  in  which  make  E  F 
equal  to  A  B,  and  F  G  equal  to  C  D. 


2.  Bisect  E  G  in  H,  and  with  H  E  or  H  G  de- 
scribe the  semicircle  E  I  G. 

3.  From  F  draw  F  I  perpendicular  to  E  G,  cutting 
the  circle  in  I,  and  I  F  will  be  the  mean  proportional 
required. 

PROBLEM  XL. 

To  find  a  line  nearly  equal  to  the  circumference 
of  its  circle,  A  BCD. 

1.  Draw  the  diameters  A  B  and  C  D  at  right 
angles. 

2.  Produce  A  B,  lill  the  part  A  G  without  be  three 
quarters  of  the  radius. 

3.  Draw  E  F  through  B,  parallel  to  C  D,  through 
G,  and  the  points  C  and  D  ;  draw  G  E  and  G  F,  cut- 
ting the  tangent  in  E  and  F ;  then  E  and  F  will  be 
equal  to  half  the  circumference. 

Much  after  the  same  manner  may  a  straight  line 
be  found  equal  to  any  part  of  a  circle,  as  is  shown  at 
Fig.  2,  but  the  following  method  is  much  better  for 
small  arcs,  as  it  requires  less  room :  — 

Remark.  —  K  any  number  of  divisions  E  I,  I  K 
K  L,  L  B,  are  taken  on  E  F,  and  from  the  points  I, 
K,  L,  lines  are  drawn  to  G,  to  cut  the  circumference 
i,  k,  I,  the  divisions  on  the  circle,  viz.,  C  i,  i  k,  k  I,  I B, 
will  be  respectively  equal  to  their  corresponding 
divisions,  E  I,  I  K,  K  L,  L  B,  on  the  tangent  line 
E  F ;  that  is,  to  k  i,  and  I  E  equal  to  i  C. 

PROBLEM   XLI. 

To  find  the   length  of  any  arc,  A  C  B,  of  a 
circle. 

1.  Draw  the  chord  A  B  indefinitely  towards  E,  and 
bisect  the  arc  A  C  B  at  C. 

2.  Make  A  D  equal  to  twice  the  half  chord 
A  C ;  divide  B  D  into  three  equal  parts,  and  set  one 
towards  E  ;  then  will  A  E  be  the  length  of  the  arc 
line  A  C  B. 


Del  iiiilii)iis 


I'KOI!  .  I. 


Ill     ll„-    l'.ll|,,M. 


IV. 


V. 


W.F.Stnttti-v  ,Si". 


PRACTICAL    GEOMETRY, 


45 


CONIC    SECTIONS. 


C  D  bisecting  the 
and  terminated  by 


OF     THE     ELLIPSIS. 

DEFINITIONS. 

Plate   5. 

1.  If  two  pins  are  fixed  at  the  points  E  and  F, 
a  string  being  put  about  them,  and  the  ends  tied 
together  at  C,  the  point  C  being  moved  round,  keep- 
ing the  string  stretched,  it  will  describe  a  cm-ve 
called  an  Ellipsis. 

2.  Foci  are  the  two  points  E  and  F,  about  which 
tlie  string  is  made  to  revolve. 

3.  Transverse  axis  is  the  line  A  B,  passing  through 
the  foci,  and  terminated  by  the  curve  at  A  and  B. 

4.  Centre  is  the  point  G,  bisecting  the  transverse 
axis  A  B. 

5.  Conjugate  axis  is  the  line 
transverse  axis  at  right  angles, 
the   curve. 

6.  Latiis  rectum  is  a  right  line  passing  through  the 
focus  F,  at  right  angles  to  the  transverse  axis,  ter- 
minated by  the  curve.  This  is  also  called  the  Pa- 
rameter, 

7.  Diameter  is  any  line  passing  through  the  centre 
G,  terminated  by  the  curve. 

8.  Conjugate  diameter  is  a  right  line  drawn  through 
the  centre,  parallel  to  a  tangent  at  the  extreme  of  the 
other  diameter,  and  terminated  by  the  curve. 

9.  Double  ordinate  is  a  line  drawn  through  any 
diameter,  parallel  to  a  tangent  at  the  extreme  of  that 
diameter,  terminated  by  the  curve. 


PROBLEMS. 

PROBLEM    I. 

The  transverse  and  conjugate  axes,  A  B,  and 
C  D,  of  an  ellipsis  being  given,  to  find  the 
two  foci,  from  thence  to  describe  an  ellipsis. 

1.  Take  the  semitransverse  A  E,  or  E  B,  and 
from  C,  as  a  centre,  describe  an  arc,  cutting  A  B  at 
F  and  G,  which  are  the  foci. 

2.  Fix  pins  in  these  points,  a  string  being  stretched 
about  the  points  F  C  G ;  then  move  the  point  C 
round  the  fbced  points  F  and  G,  keeping  the  string 


tight.     It  wUl   describe  the   ellipsis  as   in   the   first 
definition. 

PROBLEM   II. 

The  same  being  given,  as  in  the  last  problem,  to 
describe  an  ellipsis,  by  an  instrument  called  a 
trammel. 

The  trammel,  as  used  by  artificers,  is  two  rules, 
with  a  groove  in  each,  fijced  together  so  that  the 
grooves  will  be  at  right  angles  to  each  other.  To 
this  there  is  a  rod  with  two  movable  nuts,  and 
another  fixed  at  the  end,  with  a  hole  through  it, 
to  hold  a  pencil.  On  the  under  side  of  the  sliding 
nuts  are  two  round  pins,  made  to  fill  the  groove  of 
the  trammel,  and  are  used  as  follows :  — 

Operation. —  Set  the  distance  of  the  first  pin  at  B, 
from  the  pencil  at  A,  to  half  the  shortest  axis,  and 
the  distance  of  the  second  pin  at  C,  from  A,  to  half 
the  longest  axis,  the  pins  being  put  in  the  grooves, 
as  is  shown  by  the  figure  ;  then  move  the  pencil  at 
A.     It  will  describe  the  ellipsis  required. 

PROBLEM  III. 

A  diameter,  A  B,  and  a  double  ordinate,  C  D, 
to  that  diameter,  being  given,  to  find  the 
parameter. 

1.  Join  A  C,  A  D,  and  B  C,  B  D  ;  bisect  A  B  in 
H,  through  H  draw  H  I  parallel  to  D  C,  cutting 
B  C  in  I. 

2.  From  A,  make  A  F  equal  to  H  I ;  through  F 
draw  G  H  parallel  to  C  D,  cutting  A  C  in  G,  and 
A  D  in  H  ;  then  G  H  is  the  parameter  sought. 

PROBLEM  IV. 

To  describe  an  ellipsis  by  finding  points  in  the 
curve,  having  the  two  conjugate  diameters, 
A  B  and  C  D,  given. 

1.  Find  F  G  half  the  parameter  ;  through  G  draw 
H  H  parallel  to  A  B. 

2.  Draw  E  H  parallel  to  C  D,  cutting  H  H  at  I. 

3.  Set  off  any  number  of  equal  divisions  from  H 
towards  G.     Set  the  same  parts  from  E  towards  C. 


46 


PRACTICAL     GEOMETRY 


4.  From  the  point  B,  through  the  points  1,  2,  3,  in 
E  C,  draw  the  lines  B  i,  B  k,  B  /. 

5.  From  A,  through  the  poijits  in  H  G,  draw  the 
lines  A  i,  A  k,  A  I,  intersecting  the  former  lines  in 
t,  k,  I.     They  will  be  in  the  periphery  of  the  ellipsis. 

PROBLEM  V. 

Having  a  diameter,  and  a  double  ordinate  to 
that  diameter,  to  describe  the  ellipsis,  by 
finding  points  in  the  curve. 

This  problem  will  be  completed  in  the  same  man- 
ner as  Problem  IV.,  and  as  is  plainly  shown  by  the 
figures  2  and  3. 

Plate  6. 
PROBLEM   VI 

To  describe  an  ellipsis,  or  any  segment  of  an 
ellipsis,  having  a  diameter  and  a  double  ordi- 
nate, by  means  of  points  being  found  in  the 
curve,  without  finding  the  parameter. 

Let  A  B  be  the  diameter  or  double  ordinate,  let 
C  D  be  its  conjugate,  and  let  E  D  be  the  height  of 
the  segment. 

1.  Through  D  draw  F  G  parallel  to  A  B ;  also, 
through  the  points  A  and  B  draw  A  F  and  B  G, 
parallel  to  D  E,  cutting  F  G  in  F  and  G. 

2.  Divide  A  E  and  E  B  into  a  lilvc  number  of 
equal  parts,  as  four ;  likewise  B  G  and  A  F  into  the 
same  number  of  equal  parts. 

3.  From  the  point  D,  through  the  points  1,  2,  3,  in 
A  F  and  B  G,  draw  1  D,  2  D,  3  D. 

4.  From  the  point  C,  through  the  points  1,  2,  3,  in 
A  B,  draw  C  a,  C  b,  C  c ;  cutting  the  lines  1  D,  2  D, 
3  D,  in  a,  b,  c,  they  will  be  in  the  periphery  of  the 
ellipsis ;  a  curve  being  traced  througli  these  points 
will  form  the  ellipsis  required. 

But  if  the  ciirve  is  very  large,  as  in  practical 
works,  the  best  way  is  to  put  in  nails  or  pins  at  the 
points  a,  b,  c,  Sec,  bend  a  slip  round  them,  and  draw 
a  curve  by  it ;  it  will  appear  quite  regular. 

PROBLEM   VII. 

To  draw  the  representation  of  an  ellipsis,  with 
a  compass,  to   any  length,  A  B,  and  width, 
C  D. 
I.  Draw  B  P  parallel  and  equal  to  E  C,  and  bisect 

it  at  1,  then  draw  1  C  and  P  D,  cutting  each  other 


at  K ;  bisect  K  C  by  a  perpendicular,  meeting  C  D 
at  O ;  and  on  O,  with  the  radius  O  C,  describe  the 
quadrant  C  G  Q. 

Througli  Q,  and  A  draw  Q  G,  cutting  the  quad- 
rant at  G  ;  tlien  ckaw  G  O,  cutting  A  B  at  M ;  make 
E  L  equal  to  E  M ;  also  E  N  equal  to  E  O.  From 
O,  through  M  and  L,  draw  O  G  and  O  K ;  likewise 
from  N,  through  M  and  L,  draw  N  II  and  N  I ;  then 
M,  L,  N,  O,  are  the  four  centres ;  by  help  of  these, 
the  foiir  opposite  sectors  will  be  described. 

Fig.  2.  To  describe  an  ellipsis  more  accurately  with 
a  compass  than  the  foregoing,  having  the  tivo  axes 
A  B  and  C  D  given. 

1.  Draw  A  3  parallel  and  equal  to  E  C,  divide  it 
into  three  equal  parts,  and  draw  2  C  and  1  C ;  then 
divide  A  E  also  into  three  equal  parts,  and  from  D, 
through  the  points  1,  2,  in  A  E,  draw  D  Q  and  D  P, 
cutting  the  lines  1  C  and  2  C,  in  Q,  and  P. 

2.  Bisect  C  P  by  a  perpendicular,  meeting  C  D 
produced  at  S ;  join  P  S,  cutting  A  E  at  X ;  then 
make  E  W  equal  to  E  X,  and  E  U  equal  to  E  S ; 
and  through  X  and  W  draw  P  S  and  O  S  ;  also 
through  the  same  points,  X  and  W,  draw  U  K  and 
UL. 

3.  Bisect  P  Q  by  a  perpendicular,  meeting  P  S  at 
F ;  draw  Z  F  parallel  to  A  B ;  then  with  the  radius 
F  Q,  describe  the  arc  Q  Z,  cutting  F  Z  at  Z ;  through 
Z  and  A  draw  Z  y,  cutting  the  arc  Z  Q  at  y ;  and 
join  y  F,  cutting  A  B  at  V.  On  X,  malvc  X  I  equal 
to  X  F;  with  the  same  radius  on  W  make  W  H 
and  W  G ;  through  V  draw  I  R,  make  E  T  equal 
to  E  V,  through  T  draw  11  IM  and  G  N ;  then  U,  S, 
G,  H,  I,  F,  T,  V  are  the  centres. 

PROBLEM  VIII. 

Ha\'ing  the  two  axes,  or  any  other  conjugate 
diameters,  A  B  and  C  D,  given,  to  describe 
an  ellipsis  through  points,  at  the  extremes  of 
any  diameters  taken  at  pleasure. 

1.  Through  D  draw  P  Q,  parallel  to  A  B  from  D ; 
draw  D  F  perpendicular  to  P  Q,  and  make  it  equal 
to  E  B,  or  E  A;  upon  F,  with  llu-  distance  F  D,  de- 
scribe the  circle  n  D  /■'. 

2.  Through  tlie  centre  E  draw  the  line  PEN, 
<  E  M,  s  E  L,  &c.,  at  pleasure,  cutting  the  tangent 
P  Q  at  P,  t,  s,  &c.  Join  P  F,  <  F,  s  F,  &c.,  cutting 
the  circle  n  D  k.  at  the  points  m  n  I,  &c. ;  likewise 


I'l.  r, 


nioi; .  \i 


/•'if/.-4- 


//./.J. 


/>;/.•/. 


I'l   7 


TKOn.  XI. 


Xll  . 


.\1\' 


JCVl 


PRACTICAL    GEOMETRY. 


41 


join  E  F,  if  necessary,  and  draw  n  N,  vi  M,  /  L,  &c., 
parallel  to  it,  cutting  the  diameters  N  N,  M  M,  L  L, 
&c.,  at  N  M  L,  &c. ;  tlicn  these  points  will  be  in  the 
periphery  of  the  ellipsis.  If  the  diameters  arc  pro- 
duced to  the  opposite  sides,  at  N  M  L,  and  the  dis- 
tances E  N,  E  M,  E  L,  &c.,  are  made  respectively  to 
their  corresponding  opposite  distances,  E  N,  E  M, 
and  E  L,  &e.,  then  the  points  N  M  L,  on  the  under 
5ide  of  the  diameter  A  B,  will  also  be  in  the  curve. 

PEOBLEM   IX. 

To  draw  an  ellipsis  by  ordinates,  having  the 
axes,  or  any  other  conjugate  diameters,  A  B, 
and  C  D,  given. 

1.  From  E,  the  cenh-e,  cb-aw  E  F  perpendicular  to 
C  D.  Upon  E,  with  the  radius  E  C,  describe  the 
quadrant  C  F ;  divide  E  F  into  any  number  of  equal 
parts,  as  four  ;  from  these  points  draw  1  a,  2  b,  3  c, 
parallel  to  E  C,  cutting  the  quadi-ant  at  a,  b,  and  c. 

2.  Divide  E  A  and  E  B  each  in  the  same  number 
of  equal  parts ;  through  the  points  1,  2,  3,  &c.,  draw 
a  a,  b  b,  c  c,  &c.,  parallel  to  C  D. 

3.  Make  the  distances  1  a,  2  b,3  c,  See,  equal  to 
then-  coiTcsponding  distances,  1  a,  2  b,  on  the  quad- 
rant ;  then  the  points  a,  b,  c,  &c.,  will  be  all  in  the 
periphery  of  the  ellipsis. 

PROBLEM   X. 

An  ellipsis,  A  B  C  D,  being  given,  to  find  the 
transverse  and  conjugate  axes. 

1.  Draw  any  two  parallel  lines  A  B,  and  C  D,  cut- 
ting the  ellipsis  at  the  points  A,  B,  C,  D ;  bisect  them 
in  c  and/. 

2.  Through  e  and/ draw  G  11,  cutting  the  ellipsis 
at  G  and  H;  bisect  G  H  at  I;  it  will  give  the  centre. 

3.  Upon  I,  with  any  radius,  describe  a  circle,  cut- 
ting the  ellipsis  in  the  four  points,  k,  I,  m,  n. 

4.  Join  k  I,  and  m  n ;  bisect  k  I,  or  vi  n,  at  o  or  p. 

5.  Through  the  points  o  I,  or  Ip,  draw  Q,  R,  cut- 
ting the  ellipsis  at  Q  and  R ;  then  Q,  R  will  be  the 
transverse  axis. 

6.  Through  I,  draw  T  S  parallel  to  k  I,  cutting  the 
ellipsis  at  T  and  S,  and  T  S  will  be  the  conjugate 
axis. 

Plate  7. 

PROBLEM  XI. 

Any  diameter,  A  B,  being  given,  and  an  ordi- 


nate, C  D,  to  find  its  conjugate,  without  draw- 
ing any  part  of  the  ellipsis. 

1.  Draw  C  I  perpendicular  to  A  B  ;  bisect  A  B  in 
F,  and  draw  F  H  parallel  to  C  D. 

2.  On  F,  with  the  distance  F  A,  or  F  B,  describe 
the  semicircle  A  I  B,  cutting  C  I  at  I. 

3.  Make  A  E  equal  to  C  I ;  cbaw  E  G  parallel  and 
equal  to  C  D ;  through  G  and  A  draw  A  H,  cutting 
F  H  at  H ;  then  F  H  is  the  semi-conjugate. 

Much  after  the  same  manner,  if  two  conjugate 
diameters  are  given,  an  ordinate  may  be  found  with- 
out drawing  any  part  of  the  ellipsis. 

PROBLEM  XII. 

Any  two  conjugate  diameters,  A  B  and  C  D, 
being  given,  and  a  right  line,  G  H,  passing 
through  the  centre,  F,  to  find  a  diameter 
which  will  be  conjugate  to  G  H,  without 
drawing  any  part  of  the  ellipsis. 

1.  Through  D  draw  E  K  parallel  to  A  B,  and  pro- 
duce the  given  line  H  G  to  cut  the  tangent  in  E. 

2.  From  D,  make  D  I  perpendicular  to  E  F,  and 
equal  to  F  A,  or  F  B. 

3.  Join  E  I;  from  I,  di-aw  I  K  perpendicular  to 
I E,  cutting  the  tangent  E  K  at  K ;  through  the  centre 
F  draw  F  K. 

4.  Through  the  points  g-  and  m,  where  the  lines 
E  I  and  I  K  cut  the  circle,  draw  g-  G  and  vi  M  par- 
allel to  I  F,  cutting  E  F,  and  K  F,  at  the  points 
G  and  M ;  make  F  H  equal  to  F  G,  and  F  L  equal  to 
F  M ;  then  M  L  and  G  H  will  be  the  two  other 
conjugate  diameters. 

PROBLEM  XIII. 

Any  two  conjugate  diameters,  A  B  and  C  D, 
being  given,  to  find  the  two  axes,  from  thence 
to  describe  the  ellipsis. 

1.  Through  D  draw  E  F,  parallel  to  A  B ;  draw 
D  I  perpendicular  to  E  F,  and  equal  to  M  A,  or  M  B. 

2.  Upon  I,  with  the  radius  I  D,  describe  the  arc 
g-  D  /. 

3.  Join  I  M,  and  bisect  it  by  a  perpendicular,  meet- 
ing the  tangent  E  F  at  N. 

4.  On  N,  as  a  centre,  with  the  distance  N  I,  de- 
scribe a  semicircle  E  I  F,  cutting  E  F  at  the  points 
E  and  F. 


48 


PRACTICAL    GEOMETRY. 


5.  Through  the  centre  M  draw  F  K  and  E  H. 

6.  Join  I  E  and  I  F,  cutting  the  arc  g-  D  /  at 
g  and  /. 

7.  Draw  I  L  and  g  G  parallel  to  I  M,  cutting  K  F 
and  H  E  at  G  and  L.  Make  M  K  equal  to  M  L, 
and  P*I  H  equal  to  M  G ;  then  E  H  and  K  L  will  be 
the  two  axes  required. 

PROBLEM  XIV. 

An  ellipsis  being  given,  to  draw  a  tangent 
through  a  given  point  H,  in  the  curve. 

1.  Find  the  foci  F  and  G ;  join  F  H  and  G  H. 

2.  Produce  C  G  H  to  I  upon  H,  with  any  radius ; 
describe  the  arc  K  L  I,  cutting  G  I  and  F  H  at 
K  and  I. 

3.  Bisect  the  arc  K  L  I  at  L ;  through  L  and  H 
draw  L  H ;  it  will  be  the  tangent  required. 

PROBLEM  XV. 

To  draw  two  tangents  to  an  ellipsis  from  a 
given  point,  E,  without  it  having  any  two 
conjugate  diameters,  A  B  and  C  D,  given, 
without  drawing  any  part  of  the  ellipsis. 

1.  Let  the  point  E  be  in  the  diameter  D  C,  pro- 
duced. 

2.  From  the  centre  H  make  H  I  equal  to  H  C, 
and  join  I  E. 

3.  Through  C  draw  C  K  parallel  to  I  E,  cutting 
H  A  in  K. 

4.  Make  H  L  equal  to  H  K ;  through  L  chraw  F  G 
parallel  to  A  B ;  find  the  extreme  points  F  and  G  of 
the  ordinate  F  G  by  Problem  XI.  From  E,  through 
the  points  F  and  G,  draw  E  F  and  E  G.  They 
will  be  the  tangents  required. 

If  the  point  E  is  in  neither  of  the  given  diameters 
A  B  or  C  D,  when  produced,  draw  a  line  from  the 
given  point  E,  through  the  centre  ;  by  Problem  XII., 
find  a  conjugate  to  that  Line,  and  the  extremities  of 
both  ;  then  the  construction  will  be  the  same  as  in 
this. 

PROBLEM   XVL 

To  describe  an  ellipsis  similar  to  a  given  one, 
A  D  B  C,  to  any  given  length,  I  K,  or  to 
a  given  width,  M  L. 

1.  Let  A  B  and  C  D  be  the  two  axes  of  the  given 
ellipsis. 


2.  Through  the  points  of  contact,  A,  D,  B,  C, 
complete  the  rectangle  G  E  H  F ;  draw  the  diag- 
onals E  F  and  G  H.  They  will  pass  through  the 
centre  at  R. 

3.  Through  I  and  K  draw  P  N  and  O  Q  parallel 
to  C  D,  cutting  the  diagonals  E  F  and  G  II  at  P, 
N,  Q,  O. 

4.  Join  P  O  and  N  Q,  cutting  C  D  at  L  and  M ; 
then  I  K  is  the  transverse,  M  L  the  conjugate  axis 
of  an  ellipsis  that  will  be  similar  to  the  given  one, 
A  D  B  C,  which  may  be  described  by  some  of  the 


foregoing  methods. 


Plate  8. 


PROBLEM   XVII. 

Given  the  rectangle  A  B  C  D,  to  circumscribe 
an  ellipsis  which  shall  have  its  two  axes  in 
the  same  ratio  as  the  sides  of  the  rectangle. 

1.  Draw  the  diagonals  A  C  and  B  D,  cutting  each 
other  at  S,  the  centre. 

2.  Through  S  draw  E  F  and  G  H  parallel  to  A  B 
and  A  D. 

3.  Upon  S,  with  a  radius,  S  I,  equal  to  half  A  D  or 
B  C,  describe  the  quadrant  I  K  L  cutting  E  F  at  L. 

4.  Bisect  the  arc  I  K  L  at  K ;  through  K  draw 
M  N  parallel  to  E  F,  cutting  the  diagonal  B  D  at  N. 

5.  Join  I  N ;  through  B  draw  B  G  parallel  to  it, 
cutting  G  H  at  G,  and  make  S  H  equal  to  S  G. 

6.  Join  N  O  ;  through  B  draw  B  F  parallel  to  it, 
cutting  E  F  at  F ;  make  S  E  equal  to  S  F ;  then 
E  F  and  G  H  are  the  two  axes  which  may  be  de- 
scribed by  some  of  the  methods  which  are  shown  in 
the  foregoing  problems. 

PROBLEM   XVIII. 

Given  the  trapezium,  A  B  C  D,  and  a  point  E, 
in  one  of  the  sides,  to  find  a  point  in  each  of 
the  other  sides,  so  that,  if  an  ellipsis  was  to 
be  inscribed,  it  Avould  touch  the  trapezium  in 
these  points. 

1.  Produce  the  sides  of  the  trapezium  till  they 
meet  at  K  and  L. 

2.  Draw  the  diagonals  A  C  and  B  D,  cutting  each 
other  at  F  ;  produce  B  D  till  it  cut  K  L  at  M. 

3.  Through  F,  and  the  given  point  E,  draw  E  G, 
cutting  B  C  at  G. 


I'l    '!  I'liOl'.   .  X\'l\ 

c. 


XX'lil. 


XIX 


\X  1 


I   'I 


|)rl!llllliiiis. 


Ill'  llll'  I'.i  1  .ilxil.i 


ruoi'. .  1 . 


V 


11      ^v      I 


1'  !•:  f. 


V. 


•■  ii 


/■W/.  ?. 


/        or  111,-  iiv|M-ii 


PRACTICAL    GEOMETRY. 


49 


4.  From  M,  through  the  points  E  and  G,  draw 
M  H  and  M  G,  cutting  the  other  two  sides  in  the 
points  I  and  H,  then  E,  H,  G,  I,  will  be  the  four 
points  requii'cd. 

PROBLEM  XIX. 

A  trapezium,  A  B  C  D,  being  given,  and  a  point 
E,  in  one  of  the  sides,  to  find  the  centre  of 
an  ellipsis  that  may  be  described  in  the  trape- 
zium, and  pass  through  the  point  of  contact 
E,  without  dramng  any  part  of  the  ellipsis. 

1.  Find  the  points  of  contact  H,  G,  I,  E,  as  in  the 
last  problem. 

2.  Join  the  points  G  and  E  by  the  right  line  G  E, 
bisect  it  in  M,  and  from  K,  where  the  opposite  sides 
A  D  and  B  C  meet,  and  through  the  point  M,  draw 
K  M  indefinitely. 

3.  Also  join  any  other  t\.vo  points  of  contact,  as 
H  I ;  bisect  H  I  at  N,  from  L,  where  the  opposite 
sides  B  A  and  C  D  meet ;  di-aw  L  N,  meeting  K  M 
at  P ;  then  P  will  be  the  centi'c  of  the  ellipsis  re- 
quired. 

And,  in  lilce  manner,  if  the  points  G  and  H  were 
joined  and  bisected  at  Q,  and  a  line  being  drawn 
from  B  where  the  opposite  sides  A  B  and  C  D  meet 
through  Q,  it  woidd  also  meet  in  P,  the  centre,  &c. 

PROBLEM  XX. 

Given  a  trapezium,  A  B  C  D,  and  a  point  E,  in 
one  of  the  sides,  to  find  the  two  axes  of  an 
ellipsis  that  may  be  inscribed  in  the  trape- 
zium, and  pass  through  the  pomt  E  without 
drawing  any  part  of  the  ellipsis. 

1.  Find  the  opposite  pomts  of  contact,  H,  E,  F,  G, 
by  Problem  XVIII. 

2.  From  thence,  find  the  centre,  P,  by  the  last  prob- 
lem. 

3.  From  E,  and  through  the  centre,  P,  draw  E  M, 
making  P  M  equal  to  P  E. 

4.  Through  H,  or  any  other  point  of  contact,  draw 
H  K  parallel  to  D  C,  cutting  E  M  at  K ;  then  K  H 
is  an  ordinate  to  the  diameter  E  M. 

5.  Tlu-ough  P,  the  centre,  draw  P  E  parallel  to 
H  K. 

6.  Find  the  extremities  R  and  S,  of  the  diameter 
R  S,  by  Problem  XL 

7 


7.  The  conjugate  diameters  E  M  and  R  S,  being 
now  found,  then  find  the  two  axes,  V  W  and  X  Y, 
by  Problem  XIII. 

PROBLEM  XXI. 

To   find  the  centre  and  transverse  axis   of  an 
ellipsis  by  means  of  a  square  and  rule. 

1.  Apply  the  square  A  B,  Problem  XXI. 

2.  Place  the  ellipsis  tangical  to  A  B,  at  pleasure, 

3.  Draw  lines  C  D,  touching  the  opposite  sides  of 
the  ellipsis. 

4.  Draw  lines  E  F,  intersecting  the  ellipsis ;  and 
C  is  the  centre,  and  E  F  the  transverse  axis  required. 
Also,  E  F  is  equal,  added  together,  in  whatever 
direction  the  ellipsis  may  be  appHed  to  the  square 
and  rule. 


OF    THE    PARABOLA. 

DEFINITIONS. 
Plate   9. 

1.  If  a  thread,  equal  in  length  to  B  C  be  fixed  at  C, 
the  end  of  a  square,  ABC,  and  the  other  end  fixed 
at  F  ;  and  if  the  side  A  B,  of  the  square,  be  moved 
along  the  right  line,  A  D;  and  if  the  point  E  be 
always  kept  close  to  the  edge  B  C,  of  the  square, 
keeping  the  string  tight,  the  point  or  pm  E  will  de- 
scribe a  curve  E  G  I  H,  called  a  parabola. 

2.  Focus  is  the  fixed  point  F,  about  which  the 
string  revolves. 

3.  Directrix  is  the  line  A  D,  which  the  side  of  the 
square  moves  along. 

4.  Axis  is  the  line  L  K,  drawn  tlu-ough  the  focus 
F,  perpendicular  to  the  directi-is. 

5.  Vertex  is  the  point  I,  where  the  line  L  K  cuts 
the  curve. 

6.  Latus  rectum,  or  parameter,  is  the  line  G  H, 
passing  through  the  focus  F,  at  right  angles  to  the 
axis  I  K,  and  terminated  by  the  curve. 

7.  Diameter  is  any  line  M  N,  drawn  parallel  to  the 
axis  I  K. 

8.  Double  ordinate  is  a  right  line  R  S,  drawn  par- 
allel to  a  tangent  at  M,  the  exti-eme  of  the  diameter 
M  N,  terminated  by  the  curve. 

9.  Abscissa  is  that  part  of  a  diameter  contained 
between  the  curve  and  its  ordinate,  as  M  N. 


6( 


PRACTICAL    GEOMETRY. 


PROBLEMS. 


PROBLEM  I. 


To  describe  a  parabola  by  finding  points  in 
the  curve,  tlic  axis  A  B,  or  any  diameter  be- 
ing given,  and  a  double  ordinate  C  D. 

1.  Through  A  draw  E  F  parallel  to  C  D. 

2.  Through  C  and  D,  di-aw  D  F  and  C  E  parallel 
to  A  B,  cutting  E  F  at  E  and  F. 

3.  Divide  B  C  and  B  D  each  into  any  number  of 
equal  parts,  as  four. 

4.  Likewise  divide  C  E  and  D  F  into  the  same 
number  of  equal  parts,  viz.,  four. 

5.  Through  the  points  1,  2,  3,  &c.,  in  C  D,  draw 
the  lines  1  a,2b,S  c,  &c.,  parallel  to  C  D. 

6.  Also  through  the  points  1,  2,  3,  in  C  E  and  D 
F,  draw  the  lines  1  A,  2  A,  3  A,  cutting  the  parallel 
lines  at  the  points  a,  b,  c,  then  the  points  a,  b,  c  are 
in  the  curve  of  the  parabola. 

Fig.  2.  Another  method. 

1.  Join  A  C  and  A  D ;  from  A  make  A  E  equal 
to  B  C  or  B  D. 

2.  Through  A  and  E,  draw  H  I  and  F  G  parallel 
to  C  D,  cutting  A  C  and  A  D  in  the  points  F  and  G. 

3.  Through  F  and  G,  di-aw  F  H  and  G  I  parallel 
to  A  B,  cutting  H  I  at  the  points  H  and  L 

4.  From  the  points  H  and  I,  take  any  number  of 
equal  divisions  on  the  lines  H  F  and  I  G ;  from  these 
points  draw  lines  to  A. 

5.  From  B,  set  the  same  divisions  towards  C  and 
D  ;  draw  the  parallel  lines  1  a,  2  6,  3  c,  &c.,  intersect- 
ing the  former  at  the  points  a,  b,  c ;  they  will  be  in 
the  curve  of  the  parabola. 


OF     THE    HYPERBOLA. 

DEFINITIONS. 
1.  If  B  and  Care  two  fixed  points,  and  a  rule  A  B 
be  made  movable  about  the  point  B,  a  string  ADC, 
being  tied  to  the  other  end  of  the  rule,  and  to  the 
point  C,  and  if  the  point  A  is  moved  round  the  cen- 
tre B,  towards  E,  the  angle  D,  of  the  string  ADC, 
by  keeping  it  always  tight  and  close  to  the  edge  of 
the  rule,  A  B,  will  describe  a  curve,  D  F  H  G,  called 
an  hyperbola. 


2.  If  the  end  of  the  rule  at  B  was  made  movable 
about  the  point  C,  the  string  being  tied  from  the  end 
of  the  rule  A  to  B,  and  a  cui-ve  being  described  after 
the  same  manner,  it  would  be  an  opposite  hyperbola. 

3.  Foci  are  the  two  points  B  and  C,  about  which 
the  rule  and  string  revolve. 

4.  Transverse  axis  is  the  line  I  II,  terminated  by 
the  two  curves  passing  through  the  foci,  if  continued. 

5.  Centre  is  the  point  M,  in  the  middle  of  the 
transverse  axis  I  H. 

6.  Conjugate  axis  is  the  line  N  O,  passing  through 
the  centre  M,  and  terminated  by  a  circle  from  H, 
whose  radius  is  M  C,  at  N  and  O. 

7.  Diameter  is  any  line  V  W,  drawn  through  the 
centre  M,  and  terminated  by  the  opposite  curves. 

8.  Conjugate  diameter  to  another  is  the  line  drawn 
through  the  centre  parallel  to  a  tangent  with  either 
of  the  curves,  at  the  extreme  of  the  other  diameter, 
terminated  by  the  curves. 

9.  Abseissa  is  when  any  diameter  is  contained 
within  the  curve,  terminated  by  a  double  ordinate 
and  the  cm-ve,  then  the  part  within  is  called  the 
abscissa. 

10.  Double  ordinate  is  a  line  di'awn  through  any 
diameter,  parallel  to  its  conjugate,  and  terminated 
by  the  cm"ve. 

11.  Parameter,  or  latus  rectum,  is  a  line  di-awn 
through  the  focus,  perpendicular  to  the  transverse 
axis,  and  terminated  by  the  curve. 

12.  Asymptotes  are  two  right  lines  drawn  from  the 
centre  M,  and  the  points  R  S,  which  are  parallel  to 
the  conjugate  axis  N  O,  and  drawn  through  the  end 
of  the  ti'ansverse  axis  I  H;  II  R  and  H  S  being 
equal  to  M  N  or  M  O,  then  M  X  and  M  Y  are 
asymptotes. 

13.  Equilateral  or  right-angled  hyperbola  is  when 
its  transverse  or  conjugate  axes  are  equal. 

PROBLEMS. 
Plate  lO. 

PROBLEM   I. 

To  describe  an  hj^icrbola  by  finding  points  in 
the  curve  having  the  diameter,  or  axis  A  B, 
its  abscissa  B  C,  and  double  ordinate   D  E. 

1.  Through  B,  draw  G  F  parallel  to  D  E ;  from  D 
and  E,  draAv  D  G  and  E  F  parallel  to  B  C,  cutting 
G  F  in  F  and  G. 


ruoi".  .  I 


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I'l 


A 

5 


I>    J        2       J       C 


3        Z       J 


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n^  ( 


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I'KOl'..  I 


a!I(S^O®!iaS  ®1?  3®[Lfl®g. 


Ol'a  CNlnnlir 


::X 


PRACTICAL    GEOMETRY. 


51 


2.  Divide  C  D  and  C  E  each  into  any  number  of 
equal  parts,  as  four ;  through  the  points  of  division, 
1,  2,  3,  draw  lines  to  A. 

3.  Likewise  divide  D  G  and  E  F  into  the  same 
number  of  equal  parts,  viz.,  four ;  from  the  divisions 
on  D  G  and  E  F  draw  lines  to  B,  and  a  curve  being 
drawn  tlirough  the  intersections  at  B  a  ft  c  E,  wUl  be 
the  hyperbola  required. 

PROBLEM  11. 

Given  the  asjinptotes  A  B,  C  D,  and  a  point 
E,  in  the  curve,  to  describe  the  hyperbola. 

1.  Through  the  given  point  E,  di-aw  any  right  line 
E  F,  cutting  the  asymptotes  in  the  points  i  and  I. 

2.  Malce  i  F  equal  to  I  E ;  from  F  draw  as  many 
lines  as  you  please,  cutting  the  asymptotes  in  the 
points  g-,  h,  i,  k,  &c.,  and  G,  H,  I,  K,  &c. 

3.  Make  G  /,  H  /,  K  /,  &c.,  respectively,  equal  to 
g  F,  h  F,  k  F,  &c.,  through  the  points/,/,/,  describe 
a  curve,  and  it  is  the  hyperbola  required. 

In  the  same  manner  may  the  opposite  hyperbola 
be  described. 

PROBLEM  IIL 

Given  the  two  conjugate  diameters  A  B  and  C  D, 
to  find  any  number  of  j)oints  in  the  curve. 

1.  Through  B  draw  F  G  parallel  to  C  D,  make 
B  F  and  B  G  equal  to  E  C,  or  E  D  ftom  E,  tlirough 
F  and  G  di"aw  E  H,  and  E  I,  the  asymptotes. 

2.  From  A  di-aw  any  lines  A  C,  A  D,  A  E,  and 
A  F,  cutting  the  asymptotes  at  the  points  a,  a,  a,  &c., 
and  c,  d,  e,  /,  &c.  Make  the  distances  «  C,  «  D, «  E, 
a  F,  &c.,  equal  to  A  c,  A  d,  A  e,  and  A/,  &c.,  then 
the  points  C,  D,  E,  F  will  be  in  the  curve. 

Fig.  2.     Another  method. 

1.  From  the  centre  E,  draw  E  I  perpendicular  and 
equal  to  E  A  or  E  B. 

2.  Join  B  C,  take  any  number  of  points,  F,  G,  H, 
in  E  B,  and  chaw  F  /  G  g-,  H  h  parallel  to  B  C, 
cutting  E  C  at/  g-,  h. 

3.  Through/  g-,  h,  B  C,  di-aw/  A', g  I,  h  m,  i  n,  &c., 
take  the  distance  F  I,  and  make//c  equal  to  it;  then 
take  G  I,  and  make  g  I  equal  to  it ;  in  the  same 
manner,  find  the  points  m  n.  And  if  E  B  and  E  C 
are  produced  indefinitely  beyond  B  and  C,  and  lines 
be  drawn  parallel  to  B  E,  as  before,  any  number  of 
points  beyond  will  be  fomid  in  the  same  manner. 


PROBLEM  IV. 

Given  the  asymptotes,  and  a  point  in  the  curve, 
to  find  two  conjugate  diameters. 

1.  From  the  point  B,  draw  B  H  D  parallel  to  the 
asymptote  C  G.  Make  H  D  equal  to  H  B,  draw 
D  C  E,  making  C  E  equal  to  C  D.  Make  C  A  equal 
to  C  B,  then  D  E  is  the  conjugate  to  A  B. 

PROBLEM  V. 

To  describe  a  conic  section  through  five  given 
points,  A,  B,  C,  D,  E,  provided  that  all  these 
points  are  joined  by  right  lines,  and  that 
any  exterior  or  angle,  formed  by  these  lines, 
be  less  than  two  right  angles. 

1.  Join  any  four  points,  A,  B,  C,  E,  forming  the 
quadrilateral  A  B  C  E. 

2.  Through  the  fifth  point  D,  draw  D  /  and  D  g 
parallel  to  A  E  and  B  C,  meeting  A  B,  produced 
both  ways  at  the  points  /  and  g-,  if  necessary. 

3.  Also,  tln:ough  D,  draw  h  i  parallel  to  E  C, 
meetmg  B  C  and  A  E,  produced  at  the  points  h  and  i. 

4.  Divide  D  //,  D  i,  and  D/  T>  g,  into  any  number 
of  equal  parts,  as  sLx ;  likewise  divide  D  F  and  D  G 
into  the  same,  viz.,  sbc. 

5.  From  the  point  b,  and  through  the  points  1,  2, 

3,  4,  5,  in  D  i,  draw  the  lines  1  E,  2  E,  3  E,  4  E,  5  E, 
cutting  the  lines  B  a,  B  ft,  B  f,  B  d',  B  f,  and  B/  at 
the  points  a,  ft,  c,  d,  c,  draw  from  B,  through  1,  2,  3, 

4,  5,  in  D  F,  which  are  all  in  the  curve. 

In  the  same  manner,  the  points  between  B  and  D 
wiU.  be  found,  viz.,  by  drawing  Luies  from  the  points 
A  and  C,  through  the  lines  D  g  and  D  h. 

And  if  the  lines  D  i  and  D  /  are  produced,  and 

the  equal  parts,  7,  8,  9,  extended  upon  these  lines,  you 

would  obtain  as  many  points,  g^  h,  i,  &c.,  between  A 

and  B. 

Plate   11. 

PROBLEM  VI. 

To  describe  a  conic  section  to  touch  a  right 
line  A  B,  in  a  given  point  C,  to  i^ass  through 
three  other  points,  D,  E,  and  F. 

1.  Join  D  C,  E  C,  and  D  E ;  through  F  draw  F  A 
and  F  B  parallel  to  E  C  and  D  C,  cutting  A  B  at 
A  and  B. 

2.  Through  F,  draw  G  H  parallel  to  D  E,  and  pro- 
duce the  sides  C  D  and  C  E,  to  cut  it  at  G  and  H. 


52 


PKACTICAL    GEOMETRY. 


3.  Divide  F  G  and  F  H,  F  A  and  F  B,  each  into 
any  number  of  equal  parts,  as  four. 

4.  From  C,  through  1, 2,  3,  in  F  H,  draw  Ca,Cb, 
C  c,  &c. 

5.  From  E,  through  1,  2,  3,  in  F  H,  draw  1  E,  2  E, 
3  E,  &c.,  cutting  the  former  in  the  points  a,  b,  c,  which 
are  in  the  curve. 

In  the  same  manner  may  points  be  found  in  the 
other  side. 

PROBLEM  VII. 

To  describe  a  conic  section  to  touch  two  right 
lines,  A  B  and  B  C,  in  the  points  A  and 
C,  and  to  pass  through  a  given  point,  D. 

1.  Join  the  points  A  and  C;  through  D  draw  D  E 
and  D  F  parallel  to  B  A  and  B  C. 

2.  Through  D  draw  G  H,  parallel  to  A  C,  cutting 
B  A  and  B  C  in  G  and  H,  and  divide  D  G  and  D  H, 
D  E  and  D  F,  each  into  the  same  number  of  equal 
parts. 

3.  From  A,  through  the  points  1, 2, 3,  in  D  E,  draw 
the  lines  A  c,  A  6,  A  c. 

4.  From  C,  through  the  points  1, 2, 3,  in  D  H,  draw 
1  C,  2  C,  3  C,  cutting  the  former  in  a,  h,  c,  which  are 
in  the  curve. 

In  the  same  manner  may  points  be  found  between 
A  and  D. 


SECTIONS    OF    SOLIDS. 

OF   A   CYLINDER.  — DEFINITIONS. 

1.  A  cylinder  is  a  solid,  generated  by  the  revolution 
of  a  right-angled  parallelogram,  or  rectangle,  about 
one  of  its  sides ;  and,  consequently,  the  ends  of  the 
cylinder  are  equal  circles. 

2.  Axis  is  a  right  line  passing  from  the  centres  of 
the  two  circles  which  form  the  ends  of  the  cylinder. 

3.  If  a  cylinder  is  cut  by  a  plane,  parallel  to  a 
plane  passing  through  its  axis,  it  will  be  cut  in  two 
parts,  which  arc  called  segments  of  the  cylinder. 

4.  A  segment  of  a  cylinder  is  comprehended  under 
three  planes,  and  the  curve  surface  of  the  cylinder ; 
two  of  these  are  segments  of  circles :  the  other  plane 
is  a  parallelogram,  which  is  here,  for  distinction's 
sake,  called  the  plane  of  the  segment,  and  the  circu- 
lar segments  are  called  the  ends  of  the  cylinder. 


5.  The  two  sides  of  the  parallelogram,  which  is 
parallel  to  the  axis  of  the  cylinder,  are  called  the 
sides  of  the  segment  of  the  cylinder,  and  the  other 
two  sides  of  the  parallelogram  are  chords  to  the  ends 
of  the  cylinder. 

6.  If  a  cylmder,  or  segment  of  a  cylinder,  stands 
upon  one  of  its  ends,  that  end  on  wliich  it  stands  is 
called  the  base. 

7.  K  the  segment  of  a  cylinder  is  cut  obliquely  by 
a  plane,  the  intersection  of  that  plane  with  the  plane 
of  the  segment  is  called  the  chord  of  the  section. 

8.  The  section  of  a  cylinder  cut  by  any  plane  ui- 
clined  to  its  axis  is  an  ellipsis. 

This  is  proved  by  the  writers  of  conic  sections, 

PROBLEMS. 

Plate   12. 

PROBLEM  I. 

To  find  the  section  of  a  semi-cylinder,  cut  by 
a  plane  at  right  angles  to  the  plane  A  B  F  E, 
whicli  passes  through  its  axis,  making  a  given 
angle  E  F  B,  vnih.  either  of  the  sides  B  F. 

1.  Let  A  D  B  be  the  circle  of  the  base,  and  C  its 
centre. 

2.  Through  the  centre  of  the  circle  C  draw  G  D 
parallel  to  F  B,  cutting  the  circle  of  the  base  in  D, 
and  E  F  at  G ;  from  G  draw  G  H  perpendicular  to 
E  F ;  make  G  H  equal  to  C  D ;  then  E  F  is  the 
transverse  axis,  and  G  H  the  semi-conjugate. 

Or  it  may  be  described  by  ordinates,  as  in  Fig.  2, 
taken  from  the  base  and  transferred  to  the  section,  as 
the  figm*es  direct. 

Li  the  same  manner  may  any  segment  be  found, 
viz.,  by  drawing  lines  parallel  to  the  sides  of  the 
plane  of  the  segment  till  it  cut  the  chords  of  the 
section ;  from  these  points,  draw  perpendiculars  to 
the  chord ;  make  their  several  lengths  from  the  chord 
equal  to  those  of  the  base  corresponding  to  them  ;  a 
curve  line  being  drawn  through  these  points,  will  be 
the  true  section  of  the  segment  required,  as  is  plamly 
shown  by  Fig.  3. 

PROBLEM  II. 

To  find  the  tAVO  axes  of  the  section  of  a  semi- 
cylinder  cut  by  a  plane,  making  a  given 
angle  A  B  C,  with  the  plane  E  F  G  H,  pass- 


11  1. 


Si'l^A'S)^ 


I'KOIi.    I 


_sL — q|  'V  'rjii 


II . 


PRACTICAL    GEOMETRY. 


53 


ing  through  its  axis;  also  in  a  given  direc- 
tion K  I  with  the  side  K  F. 

1.  Let  E  M  F  be  the  circle  of  the  base,  and  L  its 
centre. 

2.  From  the  angular  point  B  of  the  given  angle 
ABC,  draw  B  D  perpendicvdar  to  B  A,  and  equal 
to  L  E  or  L  F,  the  radius  of  the  base ;  di-aw  D  C 
parallel  to  B  A,  cutting  B  C  at  C. 

3.  Draw  Q  R,  at  the  distance  D  C,  parallel  to  I  K ; 
through  the  centre  of  the  circle  L  draw  O  M  par- 
allel to  K  F,  cutting  the  circle  of  the  base  at  M,  and 
I  K  at  O ;  through  the  point  O  draw  O  P  parallel 
to  E  F,  cutting  Q.  R  at  P;  also  through  M  draw 
M  N  parallel  to  E  F,  from  P  draw  P  S  perpendicular 
to  Q  R,  and  P  N  parallel  to  O  M,  cutting  M  N  at 
N;  join  L  N,  cutting  the  circle  at  Z;  make  U  S 
equal  to  B  C,  and  join  O  S  upon  O  S ;  from  O, 
make  O  V  equal  to  L  Z,  then  O  V  is  the  semi- 
conjugate  axis. 

4.  Through  O  draw  W  X  perpendicular  to  O  S ; 
draw  L  T  perpendicular  to  L  N,  cutting  the  circle 
of  the  base  at  T ;  from  T,  draw  T  Y  parallel  to 
L  N,  cutting  the  base  F  E,  produced  at  Y ;  from  Y, 
draw  Y  a  parallel  to  O  JM,  cutting  K  I,  produced  at 
a;  from  a,  draw  a  W  parallel  to  O  S,  cutting  W  X 
at  W,  making  O  X  equal  to  O  W ;  then  W  X  is 
the  transverse  axis. 

PROBLEM  III. 

To  find  the  section  of  a  segment  of  a  cylinder, 
by  ordinates  cut  by  a  plane  through  a  given 
line  I  K,  in  the  plane  of  a  segment,  making 
a  given  angle  A  B  C  at  I  K,  with  the  ^jlane 
E  F  K  I. 

1.  Draw  the  tangent  Z  IVI  parallel  to  E  F,  and 
draw  O  M  parallel  to  K  F,  cutting  the  tangent  at  M, 
and  I  K  at  O. 

2.  Take  the  distance  L  M,  and  make  B  D  perpen- 
dicular to  the  angular  point  B  of  the  given  angle 
ABC  equal  to  it ;  proceed  as  in  the  last  problem ; 
Qnd  O  V  and  L  Z. 

3.  Draw  any  number  of  lines  a  a,  b  b,  c  c,  &c., 
parallel  to  O  L,  cutting  the  lines  I  K  and  E  F  at  the 
points  a,  b,  c,  &c. 

4.  From  the  points  a,  b,  c,  &c.,  in  I  K,  draw  lines 
a  1,  5  2,  c  3,  &c.,  parallel  to  O  V. 

5.  Through  the  points  a,  &,  c,  in  E  F,  draw  lines 


al,b2,c3,  &c.,  parallel  to  L  Z,  cutting  the  arc  line 
of  the  base  at  1,  2,  3,  &c. 

6.  Make  all  the  distances  a  1,  b  2,  c  3,  &c.,  from 
I  K,  equal  to  all  theur  corresponding  distances,  a  1, 
Z>  2,  c  3,  &c.,  on  the  base. 

7.  A  curve  line  being  traced  through  these  points, 
I  W  K  will  be  the  section  required. 

In  the  same  manner  the  section  of  any  irregular 
figure  may  be  found,  as  is  plainly  shown  by  Fig.  2. 

Fig.  3  shows  how  to  find  the  section  when  the 
angle  A  B  C  is  oblique. 


OF  A  CONE. 

DEFINITIONS. 

1.  A  cone  is  a  solid  figure  standing  upon  a  circu- 
lar base,  diminishing  to  a  point  at  the  top,  called  its 
vertex,  in  such  a  manner  that,  if  a  straight  line  be 
applied  from  the  vertex  round  the  circle  of  the  base, 
it  shall  coincide  every  where  with  the  curve  surface 
of  the  cone. 

2.  A  right  line  passing  through  the  cone,  from  the 
vertex  to  the  centre  of  the  circle  at  the  base,  is  called 
the  axis. 

3.  If  a  cone  be  cut  by  a  plane  not  parallel  to  its 
base,  passing  quite  through  the  curve  surface,  the 
figure  is  an  ellipsis. 

4.  If  a  cone  be  cut  by  a  plane,  parallel  to  a  plane 
touching  the  curve  surface,  the  section  is  a  parabola. 

5.  If  a  cone  be  cut  by  a  plane,  parallel  to  any 
plane  within  the  cone  that  passes  through  its  vertex, 
then  the  figure  is  an  hyperbola. 

These  three  last  definitions  are  proved  by  the 
writers  of  conic  sections. 

Note.  —  The  cone  in  the  following  problem  is  supposed  to  be  an 
upright  one. 

PROBLEM. 
Plate  12. 

PROBLEM  I. 

To  describe  the  conic  section  from  the  cone. 

Note.  —  A  D  N  is  a  section  of  the  plane,  passing  through  its  axia 
at  right  angles  with  the  sections  of  the  ellipsis,  parabola,  or  hyper- 
bola. 

For  the  Ellipsis. 
1.  Let  G  H  be  its  transverse  axis  in  the  plane 
A  D  N ;  bisect  it  at  K ;  through  K  draw  R  Q,  paral- 
lel to  A  D. 


54 


PRACTICAL    GEOMETRY. 


2.  Bisect  Q,  R  at  M;  vnth  the  radius  M  R  or  M  Q, 
describe  the  semicircle  R  P  G. 

3.  From  K,  draw  K  H  perpendicular  to  Q  R,  cut- 
ting the  cu-cle  at  H;  then  K  H  is  the  semi-conjugate 
axis,  from  which  the  ellipsis  may  be  described  as  at 
No.  1. 

For  the  Parabola. 

1,  Let  S  E  be  the  axis  of  the  parabola,  parallel  to 
the  other  side,  N  D. 

2.  From  E,  draw  E  C  at  right  angles  to  A  D,  the 
base,  cutting  the  semicu-cle  at  C ;  then  E  C  is  an  or- 
dinate or  half  the  base  of  the  parabola,  which  may 
be  described  at  No.  2. 

For  the  Hyperbola. 

1.  Let  I  F  be  the  height  of  the  hyperbola ;  pro- 
duce it  till  it  cut  the  opposite  side  A  N,  produced  at 
L ;  then  F  L  is  the  transverse  axis. 

2.  From  I,  draw  I  B  at  right  angles  to  A  D ;  then 
I  B  is  half  the  base,  which  may  be  described  as  at 
No.  3. 

XoTE.  —  The  letters  arc  made  to  eorrespond  at  No.  1,  2,  and  3, 
with,  those  of  the  cone  from  where  they  are  taken. 


OF    A    GLOBE. 

DEFINITIONS. 

A  globe  is  a  solid  figure,  and  may  be  supposed  to 
be  generated  by  the  revolution  of  a  semicircle  about 
its  diameter,  which  becomes  the  axis  of  the  globe, 
and  the  centre  of  the  semicu-cle  is  the  centre  of  the 
globe. 

Corollarij  1.  Hence  all  right  lines  drawn  from  the 
centre  to  the  circumference  of  a  globe  are  equal  to 
one  another,  for  the  semicircle  touches  the  surface  of 
the  globe  in  every  point  as  it  revolves  round. 

Corollarij  2.  The  section  of  a  globe  by  a  plane 
passing  through  its  centre  is  a  circle,  whose  diameter 
is  equal  to  the  diameter  of  the  generating  semicfrcle. 

Corollary  3.  Every  section  of  a  globe  cut  by  a 
plane  is  a  circle,  for  aU  the  lines  drawn  from  the  cen- 
tre to  its  surface  are  equal ;  consequently,  the  gen- 
erating semicircle  may  revolve  round  any  line,  as  an 
axis ;  therefore,  every  point  in  the  semicircle  will 
generate  a  circle. 

Corollary  4.  If  a  semiglobe  is  cut  at  right  angles 
to  the  plane  of  its  base,  the  section  is  a  semicircle. 


PROBLEMS. 
Plate  12. 

TROBLEM  I. 

To  find  the  section  of  a  semiglobe  at  right 
angles  to  the  plane  A  B  D,  thiough  its  cen 
tre,  and  pass  through  the  line  A  B  in  that 
plane. 

Bisect  A  B  in  D ;  on  D,  as  a  centre,  ■w^th  the  radius 
D  A,  or  D  B,  describe  the  semicircle  A  E  B,  and  it 
will  be  the  section  required. 

PROBLEM  II. 

Given  two  segments  of  cu-cles,  ABC  and 
D  E  F,  equal  or  unequal,  ha^dng  their  two 
chords,  A  C  and  D  F,  equal  to  each  other, 
and  the  segment  ABC  being  placed  upon 
D  F,  so  that  A  C  shall  coincide  with  D  F, 
and  the  segment  A  B  C  at  right  angles  to 
D  E  F,  to  find  the  radius  of  a  globe,  so  that 
the  arc  Imcs  ABC  and  D  E  F  shall  be  in 
its  surface  when  the  two  segments  are  placed 
in  the  above  position. 

1.  Make  a  rectangle  A  D  F  C,  so  that  the  opposite 
sides,  A  C  and  D  F,  will  be  the  bases  of  *the  segments 
A  B  C  and  D  E  F. 

2.  Find  the  centres  G  and  H  of  these  segments. 

3.  Through  H  draw  I  K  parallel  to  G  F,  and  com- 
plete the  semicircle  I  D  E  F  K. 

4.  Through  G  or  H  di-aw  H  L  parallel  to  G  F, 
cutting  A  C  and  I  K  at  L  and  H ;  make  H  ]\I  equal 
to  L  G,  join  M  K  or  M  I,  and  it  will  be  the  radius 
required. 

If  upon  E,  as  a  centre,  with  the  distance  M  I,  or 
M  K,  a  segment  I  N  K  is  described,  it  will  be  part 
of  the  greatest  circle  that  can  be  drawn  in  the  globe. 

PROBLEM  III. 

A  figure  being  generated  by  the  revolution  of  a 
plain  figure,  ha^ing  two  perpendicular  legs, 
and  the  other  side  being  irregular,  or  straight, 
or  a  curve  Hue  of  any  kind,  the  figure  bemg 
made  to  revoh"e  about  one  of  its  perpendicu- 
lar legs.  To  find  the  figure  of  the  section, 
cut  any  where  across  the  base  and  right  an- 


SE©ini®RlS  (j&i?  3®ILaiDS. 


i'l.l.t 


^•\  c^-liiuLfr  aTi<l  its    Sections  .  F«j;e   Ij. 


A  ( '  one  and  its  Sectioius  .  Rige  47. 


j\  Sphere  or  r.li:)be. 


A  Splieroid  &'! 


PRACTICAL    GEOMETRY. 


55 


gles  to  the  plane  of  the  base,  havhig  that  sec- 
tion which  passes  through  the  axis. given. 

1.  Let  A  F  E  G  B  be  the  cu-cle  of  the  base,  and 
let  the  section  required  be  cut  across  F  G ;  also  let 
A  B  C  be  a  section  of  the  soUd  passing  tlnough  the 
axis. 

2.  From  the  centre  O,  draw  the  concentric  cncles 
H  //,  It,  K  k,lj  I,  to  cut  A  B,  in  the  points  H,  I,  K,  L, 
and  F  G,  in  the  points  h,  i,  k,  I. 

3.  Erect  perpendiculars  to  the  lines  A  B  and  F  G, 
both  ways  from  these  points,  to  cut  A  C  in  H,  I, 
K,  L. 

4.  Make  the  distances  h  Ji,  i  i,  k  k,  1 1,  equal  to  their 
corresponding  distances  H  H,  1 1,  K  K,  L  L  ;  a  cmve 
being  drawn  through  these  points,  it  will  be  the  sec- 
tion reqvured. 

If  the  given  section  is  triangle,  the  section  is  an 
upright  hyperbola. 

K  the  given  section  is  a  semicncle,  the  required 
section  will  also  be  a  semicircle  ;  these  appear  plain 
by  the  figures,  and  m  this  case  there  is  no  tracing 
required. 


OF     A     SPHEEOID. 

DEFINITIONS. 

1.  A  spheroid  is  a  soUd,  generated  by  the  rotation 
of  a  semi-ellipsis  about  the  transverse  or  conjugate 
axis,  and  the  centre  of  the  ellipsis  is  the  centre  of 
the  spheroid. 

2.  The  line  about  which  the  ellipsis  revolves  is 
called  the  axis. 

3.  If  the  spheroid  is  generated  about  the  conjugate 
axis  of  the  semi-eUipsis,  then  it  is  called  a  prolate 
spheroid. 

4.  K  the  spheroid  is  generated  by  the  semi-ellipsis 
about  the  transverse  axis,  then  it  is  called  an  oblate 
spheroid. 

Proposition  1.^  Every  section  of  a  spheroid  is  an 
ellipsis,  except  when  it  is  perpendicular  to  that  axis 
about  which  it  is  generated,  in  wliich  case  it  is  a 
circle. 

Proposition  2.  —  All  sections  of  a  spheroid  parallel 
to  each  other  are  similar  figures. 

Proposition  3.  —  If  a  semi-spheroid  is  cut  by  a  plane 


at  right  angles  to  the  base,*  then  the  section  is  a 
semi-ellipsis,  and  tlic  intersection  with  the  base  will 
be  one  of  its  axes  ;  and  if  a  line  is  drawn  perpendic- 
ular from  the  middle  of  that  intersection  to  the  base 
of  the  spheroid,  to  cut  its  surface,  that  line  will  be 
half  the  other  axis,  whether  transverse  or  conjugate. 

PROBLEMS. 

Plate   13. 

PROBLEM  I. 

Given  the  base  A  D  B  C,  which  is  a  section 
through  the  longest  axis  of  an  oblong  sphe- 
roid, to  find  the  foiTn  of  the  section,  by  cut- 
ting the  base  through  the  line  E  F,  at  light 
angles  to  its  plane. 

1.  Let  A  B  be  the  transverse,  and  C  D  the  conju- 
gate axis  of  the  base;  through  the  centi-e  G  draw 
H  I  parallel  to  the  given  direction  E  F,  cutting  the 
ellipsis  at  the  poiiits  H  and  I. 

2.  Produce  E  F  towards  K ;  make  Q,  K  equal  to 
G  H  or  G  I ;  and  erect  the  perpendicular  K  M. 

3.  Make  K  M  equal  to  C  G  or  G  D,  and  bisect 
E  F  at  Q,  and  draw  M  Q.  Erect  the  perpendicular 
F  P,  cutting  M  Q  at  the  point  P,  through  Q, ;  draw 
Q,  R  parallel  and  equal  to  K  M ;  then  Q,  R  will  be 
the  semi-conjugate,  and  E  F  the  transverse  axis  of 
the  section  requfred,  from  which  the  ellipsis  may  be 
described  by  any  of  the  foregoing  methods. 

PROBLEM  II. 

To  find  the  length  of  any  arc  A  B  C,  of  a  cir- 
cle mechanically,  very  near ;  or  to  transfer 
the  same  on  the  circumference  of  another 
cu-cle  F  G  H,  of  a  difierent  radius,  from  a 
given  point  F. 

1.  Take  your  compass  at  any  small  opening,  be- 
ginning at  A,  and  take  the  equal  parts,  1,  2,  3,  4,  5, 
6,  on  the  arc  ABC. 

2.  From  D,  lay  the  same  number  of  equal  parts 
on  the  right  line  D  E,  towards  E,  viz.,  1,  2,  3,  4,  5,  6, 
and  from  the  arc  ABC  take  the  remaining  part 
B  C,  and  place  it  on  the  right  line  D  E,  from  6  to  E ; 

*  It  is  here  meant  that  the  base  is  a  section  made  by  a  plane, 
passing  through  the  centre  of  the  spheroid,  at  right  angles  to  the 
transverse  or  conjugate  axis  of  the  spheroid. 


56 


PRACTICAL    GEOMETRY 


then  will  the  length  of  the  right  line  D  E  be  nearly 
equal  to  the  arc  A  B  C  stretched  out. 

In  the  same  manner  may  A  B  C  be  transferred  to 
the  cncle  F  G  H,  viz.,  by  taking  the  divisions,  1,  2, 
3,  4, 5, 6,  and  beginning  at  F,  with  the  same  opening 
of  your  compass,  setting  off  the  divisions,  1,  2,  3,  4, 
5,  6,  on  the  arc  F  G  H,  and  transferring  the  part  6  C 
to  6  H,  as  before ;  then  ^vtII  the  arc  F  G  H  be  equal 
to  tlie  arc  ABC. 


OF  A  CYCLOID  OR  EPICYCLOID. 

DEFINITION. 

A  cycloid  or  epicyloid  is  a  figure  generated  by  a 
circle  rolling  along  the  straight  edge  of  a  ruler,  or 
another  circle  at  rest,  while  a  point  in  the  circumfer- 
ence describes  a  figm'c  on  the  plane  called  a  cycloid 
or  epicycloid. 

PROBLEMS. 
Plate  13. 

PROBLEM  I. 

To  describe  a  cycloid. 

1.  Let  B  C  be  the  edge  of  a  sti-aight  ruler;  erect 
A  D  perpendicular  to  B  C,  equal  to  tlie  diameter  of 
the  generating  circle ;  upon  the  diameter  A  D  de- 
scribe a  circle ;  tlurough  the  centre,  at  E,  draw  Q,  E. 
parallel  to  B  C. 

2.  Divide  the  semi-circumference  D  1  2  3,  &c.,  to 
A,  into  equal  parts,  and  lay  the  same  number  of  equal 
parts  upon  the  right  line  A  B,  from  A  towards  B ; 
from  all  the  divisions  on  A  C  erect  perpendiculars, 
cutting  Q  R  at  tlie  points  F,  G,  H,  &c. 

3.  With  the  radius  E  D  or  E  A,  on  the  points 
F,  G,  H,  &c.,  as  centres,  describe  arcs  1  /,  2  g-,  3  h, 
&c.;  take  the  chords  A  1,  A 2,  A3,  &c.,  from  the  semi- 
circle ;  make  tlie  distance  1  /,  2  g-,  3  h,  &c.,  respec- 
tively to  them,  then  these  points  will  be  in  the  ciuve 
of  the  cycloid. 

rROBLEM  II. 

To  describe  an  epicycloid. 

1.  Let  B  A  C  be  the  edge  of  the  circle  round  which 
the  other  circle  is  to  turn ;  through  the  centre  S  and 
the  point  A,  in  the  circuraierencc,  draw  the  right  line 


S  D ;  make  A  D  equal  to  the  diameter  of  the  gen- 
erating circle. 

2.  Divide  the  circumference  D  1  2  3,  &c.,  into 
equal  parts,  and  place  them  upon  the  arc  A  C,  from 
A  to  1,  2,  3,  &c.,  to  8. 

3.  With  the  radius  S  E,  on  the  centre  S,  describe 
the  arc  Q  R ;  through  the  centre  S  and  the  points 
1,  2,  3,  &c.,  draw  lines,  cuttmg  Q  R  at  F,  G,  H,  &c., 
and  proceed  in  every  other  respect,  as  in  the  cycloid, 
and  you  will  get  the  curve. 


SECTION    OF    PLANES. 

Of  the  Positions  of  Lines  and  Planes,  and  the  Prop' 
erties  arising  from  their  Intersections. 

DEFINITIONS. 

1.  A  plane  is  a  surface  in  which  a  straight  line 
may  coincide  in  all  dii-ections. 

2.  A  straight  line  is  in  a  plane  when  it  has  two 
points  in  common  with  that  plane. 

3.  Two  sti-aight  lines  which  cut  each  other  in  space, 
or  woidd  intersect,  if  produced,  are  in  the  same  plane ; 
and  two  lines  that  are  parallel  are  also  in  the  same 
plane. 

4.  Three  points  given  in  space,  and  not  in  a  sti-aight 
line,  are  necessary  and  sufficient  for  determining  the 
position  of  a  plane.  Hence  two  planes  which  have 
tliree  points  common  coincide  with  each  other. 

5.  The  intersection  of  two  planes  is  a  sti'aight  line. 

PROBLEM. 
Plate  14. 

^Vlien  two  planes  A  B  C  D,  A  B  F  E,  (Fig.  1,) 
intersect,  tlicy  form  between  them  a  certain 
angle,  wliicli  is  called  the  inclination  of  the 
two  planes,  and  -n-hich  is  measured  by  the 
angle  contained  by  two  lines  ;  one  drawn  in 
each  of  the  planes,  perpendicular  to  their 
line  of  common  section. 

1.  Thus,  if  the  line  A  F,  in  the  plane  A  B  E  F,  be 
perpendicular  to  A  B,  and  the  line  A  D,  in  the  plane 
A  B  C  D,  be  the  perpendicular  also  to  A  B,  then  the 
angle  F  A  D  is  the  measure  of  the  inclination  of 
the  planes  A  B  E  F,  A  B  C  D.     When  the  angle 


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PRACTICAL     GEOMETRY. 


57 


F  A  D  is  a  right  angle,  the  two  planes  are  perpen- 
dicular. 

2.  (Fig.  2.)  A  line,  A  B,  is  perpendicular  to  a  plane 
P  Q,  when  the  line  A  B  is  perpendicular  to  any  line 
B  C,  in  the  plane  P  Q,  which  passes  through  the 
point  B,  where  the  line  meets  the  plane.  The  point 
B  is  called  the  foot  of  the  perpendicular. 

3.  A  line  A  B  (Fig.  8)  is  parallel  to  a  plane 
P  Q,  when  the  line  A  B  is  parallel  to  another  straight 
line  C  B,  in  the  plane  P  Q,. 

4.  If  a  straight  line  have  one  of  its  intermediate 
points  in  common  with  a  plane,  the  whole  line  will 
be  in  the  plane. 

5.  Two  planes  are  parallel  to  one  another  when 
they  cannot  intersect  in  any  direction. 

6.  The  intersections  of  two  parallel  planes  with  a 
third  are  parallel.  Thus,  in  Fig.  4,  the  lines  A  B, 
C  D,  comprehended  by  the  parallel  plane  P  Q,  R  S, 
are  parallel. 

7.  Any  number  of  parallel  lines,  comprised  be- 
tween two  parallel  planes,  are  equal.     Thus,  Fig.  5, 

the  parallel  lines  A  a,  B  b,  C  c, ,  comprised 

by  the  parallel  planes  P  Q,  R  S,  are  all  equal. 

8.  If  two  planes  C  D  E  F,  G  H  I  J,  Fig.  6,  are 
perpendicular  to  a  third  plane,  P  Q,  their  intersection, 
A  B,  will  be  perpendicular  to  the  third  plane  P  Q. 

9.  If  two  straight  lines  be  cut  by  several  parallel 
planes,  these  straight  lines  will  be  divided  in  the 
same  proportion. 


GENERAL  APPLICATION  OF  THE  TRE- 
HEDRAL  TO  TANGENT  PLANES. 

PROBLEM. 

Plate  14. 

Given  the  inclination  and  seat  of  the  axis  of  an 
oblique  cylinder  or  cylindroid,  to  find  the 
angle  which  a  tangent  makes  at  any  point  in 
the  circumference  of  the  base,  with  the  plane 
of  the  base. 

1.  (Figs.  1,  3,  Plate  14.)  Let  A  E  B  O  be  the  base 
of  the  cylinder  or  cylindroid,  C  B  the  seat  of  the  axis, 
and  let  B  C  D  be  the  angle  of  inclination,  and  let  O 
be  the  point  where  the  tangent  plane  touches  the 
curved  surface  of  the  solid. 

R 


2.  Draw  O  N  a  tangent  line  at  the  point  O  in  the 
base,  and  draw  O  P  parallel  to  C  B.  Make  the  angle 
P  O  R  equal  to  B  C  D,  and  draw  P  R  perpendicular 
to  P  O. 

3.  Then  if  the  triangle  P  O  R  be  conceived  to  be 
revolved  round  the  line  P  O,  as  an  axis,  until  its  plane 
becomes  perpendicular  to  the  plane  of  llic  circle 
A  E  B  C,  the  straight  line,  O  R,  will,  in  this  position, 
coincide  with  the  cylincWcal  surface,  and  a  plane 
touching  the  cylinder  or  cylindroid  at  ()  will  pass 
through  the  lines  O  N  and  O  R.  Here  will  now  be 
given  the  two  legs,  P  O  R  and  P  O  N,  of  a  right- 
angled  trehedral  to  find  the  angle  which  the  hypothe- 
nuse  makes  with  the  base.  Draw  P  Q,  perpendicular 
to  O  N,  intersecting  it  in  7n,  and  draw  P  S  perpen- 
dicular to  P  Q.  Make  P  S  equal  to  P  R,  and  join 
VI  S ;  then  P  m  S  is  the  angle  required. 

4.  The  hypothenuse  will  be  easily  constructed  at  the 
same  time,  thus :  make  m  Q,  equal  to  tn  S,  and  join 
O  Q,  then  N  O  Q  will  be  the  hypothenuse  required. 

5.  In  Fig.  1,  the  method  of  finding  the  angle  which 
the  tangent  plane  makes  with  the  base  and  the  hypoth- 
enuse is  exhibited  at  four  different  points.  In  the  first 
two  points,  O  from  A,  in  the  first  quadrant,  the  tan- 
gent planes  make  an  acute  angle  at  each  point  O ; 
but  in  the  second  quadrant,  they  make  an  obtuse 
angle  at  each  point  O. 

6.  Fig.  2  is  the  second  position  of  the  construction 
from  the  point  A,  for  finding  the  angle  which  the 
tangent  plane  makes  with  the  base,  and  for  finding 
the  hypothenuse  enlarged ;  in  order  to  show  a  more 
convenient  method  by  not  only  requu'ing  less  space, 
but  less  labor,  it  may  be  thus  described,  the  two  given 
legs  P'  Q'  R'  and  P'  O'  N'. 

7.  Draw  P'  m'  perpendicular  to  O'  N',  meeting 
O  N  in  m'.  In  P'  O',  make  P'  v'  equal  to  P'  m',  and 
draw  the  straight  line  v'  R',  then  P'  v'  R'  will  be  the 
inclination  of  the  tangent  plane  at  the  point  O. 

8.  Again :  in  O'  P'  make  O'  t'  equal  to  O'  m',  and 
draw  i'  u'  parallel  to  P'  R'.  From  O',  with  the  radius 
O'  R',  describe  an  arc  meeting  i'  u'  in  ti',  and  draw 
the  straight  line  O'  u' ;  then  t'  O'  u'  is  the  hypothenuse. 

9.  For  since  P'  S'  is  equal  to  P'  R',  and  P'  v'  equal 
to  P'  ?«',  and  the  angles  m'  P'  S'  and  v'  P'  R'  are 
right  angles ;  therefore,  the  triangle  v'  P'  R'  is  equal 
to  the  triangle  m'  P'  S',  and  the  remaining  angles  of 
the  one  equal  to  the  remaining  angles  of  the  other, 
each  to  each  ;  hence  the  angle  P'  v'  R'  is  equal  to  the 
angle  P'  m'  S'. 


58 


PRACTICAL    GEOMETRY. 


10.  Again :  because  O'  t'  is  equal  to  O'  m',  and  O' 
Q,'  is  equal  to  O'  R',  and  O'  u'  is  also  equal  to  O'  R', 
therefore  O'  u'  is  equal  to  O'  Q' ;  and  since  the  angles 
O'  t'  u'  and  O'  m'  Q,'  are  each  a  right  angle,  therefore 
the  t\vo  right-angled  triangles  have  their  hypothenuses 
equal  to  each  other,  and  have  also  one  leg  in  each 
equal  to  each  other  ;  therefore  the  remaining  side  of 
the  one  triangle  is  equal  to  the  remaining  side  of  the 
other,  and  therefore,  also,  the  angles  which  are  oppo- 
site to  the  equal  sides  are  equal;  hence  the  angle 
P'  O'  w'  is  equal  to  N'  O'  Q'. 

11.  By  considering  this  construction  by  the  trans- 
position of  the  triangles,  the  whole  of  the  angles 
which  the  tangent  planes  make  at  a  series  of  points 
O,  in  figures  1  and  3,  their  hypothenuses  may  be  all 
found  in  one  diagram,  as  in  Fig.  4. 

12.  Thus,  in  Fig.  4,  if  the  angles  A  C  O,  A  C  O' 
A  C  O",  A  C  O'",  be  respectively  equal  to  A  C  O, 
A  C  O',  A  C  O",  A  C  O'",  Fig.  1,  and  in  Fig.  4,  the 
semicircle  A  O'  B  be  described,  and  if  C  D  be  drawn 
perpendicular  to  A  B,  and  the  angles  CAD,  C  B  D, 
be  made  equal  to  BCD,  Fig.  1,  then  each  half 
of  Fig.  4,  being  constructed  as  in  Fig.  2,  the  angles 
at  m  m'  m"  m'"  will  be  respectively  equal  to  the 
angles  P  m  S,  P'  m'  S',  Q"  m"  S",  Q"  m'"  S",  in  Fig.  1. 

Also,  in  Fig.  4,  the  angles  C  A  E,  C  Ag-,  C  A  /(, 
C  B  t,  C  B  k,  C  B  F  will  be  the  hypothenuses  at  the 
points  A,  O,  O',  O",  0"\  B,  in  Fig.  1. 

We  may  here  observe.  Fig.  1,  that  the  angles 
which  the  tangent  planes  make  with  the  plane  of  the 
base  in  the  first  quadrant  are  acute ;  and  those  in  the 
second  quadrant  arc  obtuse ;  and  those  in  the  second 
quadrant  arc  the  supplements  of  the  angles  V  m  S ; 
and,  moreover,  that  all  the  angles  which  constitute 
the  hypothenuses  of  the  trehedral  are  all  acute, 
whether  in  the  first  quadrant  or  the  second  quadrant 
of  the  semicircle  A  O  B. 


SECTIONS 
On  the  projection  of  a  straight  line  bent  vpon  a  cylin- 
dric  surface,  and  the  method  of  draiving  a  tangent 
to  such  a  projection. 

Plate   14. 

PROBLEM  I. 

Given   the    development  of  the  surface  of  the 
semi-cylinder,  and  a  straight  line  in  the  devel- 


opment, to  find  the  projection  of  the  straight 
line  on  a  plane  passing  through  the  axis  of 
the  cyliuder,  supposing  the  development  to 
incase  the  semi-cylincbic  surface. 

Fig.  5.  Let  A  B  C  be  the  development  of  the 
cylindric  surface,  B  C  being  the  development  of  the 
semi-circumference,  and  let  A  C  be  the  straight  line 
given. 

Produce  C  B  to  D,  making  B  D  equal  to  the  diam- 
eter of  the  cylinder.  On  B  D,  as  a  diameter,  describe 
the  semicircle  BED,  and  divide  the  semicircular  arc 
BED  into  any  number  of  equal  parts,  at  1,  2,  3, 
&c.,  and  its  development  B  C  into  the  same  number 
of  equal  parts,  at  the  points  /,  §•,  h,  &c.  Draw  the 
straight  lines  /  /.-,  g  I,  h  m,  &c.,  parallel  to  B  A,  meet- 
ing A  C  at  the  points  k,  I,  m,  &c. ;  also  parallel  to 
B  A  draw  the  straight  lines  1  o,  2  p,  S  q,  &c.,  and 
draw  ko,  Ip,  m  q,  &c.,  parallel  to  C  D ;  and  the 
points  o,p,  q,  &c.,  are  the  projections  or  seats  of  the 
points  k,  I,  m,  &c.,  in  the  development  of  the  straight 
line  A  C. 

The  projection  of  a  screw  is  found  by  this  method : 
B  D  may  be  considered  as  the  diameter  of  the  cylin- 
der from  which  the  screw  is  formed ;  and  the  angle 
B  A  C  the  inclination  of  the  thread,  with  a  straight 
line  on  the  surface ;  or  B  C  A  the  inclination  of  the 
thread  with  the  end  of  the  cylinder.  The  same  prin- 
ciple also  appUes  to  the  delineations  of  the  hand  rails 
of  stairs,  and  in  the  construction  of  bevel  bridges,  of 
which  we  shall  treat  in  a  subsequent  part  of  this 
work. 

PROBLEM  II. 

Given  the  entire  projection  of  a  helix  or  screw, 
in  the  surface  of  a  semi-cylinder,  and  the 
projection  of  a  circle  in  that  surface  perpen- 
dicular to  the  axis,  upon  the  plane  passing 
through  the  axis,  to  draw  a  tangent  to  the 
curve  at  a  given  point. 

Fig.  6.  Let  B  P  K  be  the  projection  of  the  helix 
or  screw,  and  B  A  the  projection  of  the  circumference 
of  a  circle,  and  since  this  circle  is  in  a  plane  perpen- 
dicular to  the  plane  of  projection,  it  will  be  projected 
into  a  straight  line  A  B,  equal  to  the  diameter  of  the 
cylinder. 

On   A  B,  as  a  diameter,  describe  the   semicircle 


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PRACTICAL     GEOMETRY. 


59 


A.  r  B,  and  draw  P  r  perpendicular  to,  and  inter- 
secting, A  B  in  q,  join  tlio  points  e  r,  and  produce 
e  r  to  /. 

Produce  A  B  to  C,  so  that  B  C  may  be  equal  to 
the  semicircular  arc  B  r  A.  Draw  C  D  perpendic- 
ular to  B  C,  and  make  C  D  equal  to  A  K,  and  draw 
the  straight  line  B  D ;  then  B  D  will  be  the  devel- 
opment of  the  curve  line  B  P  K. 

Dra\\-  P  ti  parallel  to  A  C,  meeting  B  D  in  u,  and 
draw  u  t  perpendicular  to  B  C.  Draw  r  g  perpen- 
dicular to  e  ;•,  and  make  r  g  equal  to  B  t.  Draw  g  n 
perpendicular  to  A  C,  meeting  B  C  in  n,  and  draw 
the  straight  line  n  P ;  then  n  P  will  touch  the  curve 
at  the  point  P. 

Or  the  tangent  may  be  drawn  independent  of 
BCD,  thus :  Draw  P  r  perpendicular  to  A  B,  and  r  g 
a  tangent  at  r.  Make  r  g  equal  to  the  development 
of  r  B,  and  draw  g  n  perpendicular  to  B  C,  meet- 
ing B  C  in  n,  and  join  n  P,  which  is  the  tangent 
required. 


PEELIMINARY    PRINCIPLES 
OF    PROJECTION. 

PROBLEM. 
Plate  15. 

If  from  a  point  A',  Fig.  1,  in  space,  a  perpendic- 
ular A'  a  be  let  fall  to  any  plane  P  Q  whatever,  the 
foot  a  of  this  perpendicular  is  called  the  projection 
of  the  point  A'  upon  the  plane  P  Q. 

K,  through  different  points  A',  B',  C,  D',....Figs. 
2,  3,  4,  of  any  line  A',  B',  C,  D',  .  .  .  .  whatever  in 
space,  perpendiculars   A'  o,  B'  b,  C  c,T>'  d,  . 
be  let  fall  upon  any  plane  P  Q,  whatever,  and  if 

tlu-ough  a,  b,  c,  d, the   projections  of  the 

points  A',  B',  C,  D',  iji  the  plane  P  Q,  a  line  be 
drawn,  the  line  thus  drawn  will  be  the  projection  of 
the  line  A'  B'  C  D'  .  .  .  .  given  in  space. 

If  the  line  A'  B'  C  D'  .  .  .  .  Fig.  3,  be  straight, 
the  projection  abed.  .  .  .  will  also  be  a  straight 
line ;  and  if  the  line  A'  B'  C  D'  .  .  .  .  Fig.  2,  be  a 
curve  not  in  plane  perpendicular  to  the  plane  P  Q, 
the  curve  abed....  which  is  the  projection  of 
the  curve  A'  B'  CD',....  in  space,  will  be  of  the 
same  species  with  the  original  curve,  of  which  it  is 
the  projection.     Hence,  in  this  case,  if  the  original 


curve  A'  B'  C  D'  .  .  .  .  be  an  ellipse,  a  parabola,  an 
hyperbola,  &c.,  the  projection  abed....  will  be 
an  ellipse,  a  parabola,  an  hyperbola,  &c.  The  circle 
and  the  ellipse  being  of  the  same  species,  the  pro- 
jected curve  may  be  a  circle  or  ellipse,  whether  the 
original  be  a  circle  or  ellipse,  as  in  Fig.  4. 

The  plane  in  which  the  projection  of  any  point, 
line,  or  plane  figure  is  situated  is  called  the  plane  of 
projection,  and  the  point  or  line  to  be  projected  is 
called  the  primitive. 

The  projection  of  a  curve  will  be  a  straight  line 
when  tlie  curve  to  be  projected  is  in  a  plane  perpen- 
dicular to  the  plane  of  projection.  Hence  the  pro- 
jection of  a  plane  curve  is  a  straight  line. 

If  a  curve  be  situated  in  a  plane  which  is  parallel 
to  the  plane  of  projection,  the  projection  of  the  curve 
will  be  another  curve  equal  and  similar  to  the  curve 
of  which  it  is  the  projection. 

The  projection  upon  a  plane  of  any  curve  of  double 
curvature  whatever  is  always  a  curve  line. 

In  order  to  fi:x  the  position  and  form  of  any  line 
whatever  in  space,  the  position  of  the  line  is  given  to 
each  of  two  planes  which  are  perpendicular  to  each 
other ;  the  one  is  called  the  horizontal  plane,  and  the 
other  the  vertical  plane ;  the  projection  of  the  line  in 
question  is  made  on  each  of  these  two  planes,  and 
the  two  projections  are  called  the  two  projections  of 
the  line  to  be  projected. 

Thus  we  see,  in  Fig.  5,  where  the  parallelogram 
U  V  W  X  represents  the  horizontal  plane,  and  the 
parallelogram  U  V  Y  Z  represents  the  vertical  plane ; 
the  projection  a  b  ot  the  line  A'  A'  in  space  upon  the 
horizontal  plane  U  V  W  X  is  called  the  horizontal 
projeetion;  and  the  projection  A  B,  of  the  same  line 
upon  the  vertical  plane  U  V  Y  Z,  is  called  the  verti- 
eal  projeetion. 

The  two  planes  upon  which  we  project  any  line 
whatever  are  called  the  planes  of  projection. 

The  intersection  U  V  of  the  two  planes  of  projec- 
tion, is  called  the  ground  line. 

When  we  have  two  projections  a  &,  A  B  of  any  line 
A  B'  in  space,  the  line  A'  B'  will  be  determined  by- 
erecting  to  the  planes  of  projection  the  perpendiculars 
a  A,  i  B' . .  .  A  A',  B  B' .  .  .  through  the  projections 

a,b, A,  B, of  the  original  points  A',  B'. 

of  the  line  in  question.     For  the  perpendiculars 

a  A',  A  A'  erected  from  the  projections  a,  A  of  the 
same  point  A'  will  intersect  each  other  in  space  in  a 
point  A',  which  will  be  one  of  these  in  the  line  \v 


60 


PRACTICAL    GEOMETRY. 


question.  It  is  clear  tiiat  the  other  points  must  be 
found  in  the  same  manner  a.s  this  which  has  now 
been  done. 

When  we  iiavc  obtained  the  two  projections  of  a 
line  in  space,  whether  immediately  from  the  line  it- 
self or  by  any  other  means  whatever,  we  must  aban- 
don this  line  in  order  to  consider  its  two  projections 
only,  since,  when  we  design  a  working  drawing,  we 
operate  only  upon  the  two  projections  of  this  line 
that  we  have  brought  together  upon  one  plane,  and 
we  no  longer  see  any  thing  in  space. 

However,  to  conceive  that  which  we  design,  it  is 
absolutely  necessary  to  carry  by  thought  the  opera- 
tions into  space  from  their  projections.  This  is  the 
most  difficult  part  that  a  beginner  has  to  surmount, 
particularly  when  he  has  to  consider  at  the  same 
time  a  great  number  of  lines  in  various  positions 
in  space. 

The  perpendicular  A-  a,  Fig.  5,  let  fall  from  any 
point  A  whatever  in  space  upon  the  plane  X  V  of 
projection,  is  called  the  projectant  of  the  point  A' 
upon  this  plane.  Moreover,  the  perpendicular  dis- 
tance between  the  point  A'  and  the  horizontal  plane 
X  V,  is  called  the  projectant  upon  the  horizontal 
plane,  or  simply  the  horizontal  projectant;  and  the 
perpendicular  distance  A'  A  between-  the  original 
point  A'  and  the  vertical  plane  U  Y,  is  called  the  pro- 
jectant upon  the  vertical  plane,  or  simply  the  vertical 
projection. 

We  shall  rcmarlc,  so  as  to  prevent  any  mistake, 
that  the  horizontal  projectant  A'  a  is  the  perpendic- 
ular let  fall  from  the  original  point  upon  the  horizon- 
tal plane,  and  that  the  vertical  projectant  is  the  per- 
dicular  let  fall  from  that  point  upon  the  vertical  plane. 
Hence  the  horizontal  projectant  is  parallel  to  the  ver- 
tical plane,  and  is  equal  to  the  distance  between  the 
original  point  and  the  horizontal  plane;  and  the  ver- 
tical projectant  is  parallel  to  the  horizontal  plane,  and 
is  equal  to  the  distance  between  the  original  point 
and  the  vertical  plane. 

We  may  remark,  that  if  through  a.  Fig.  G,  the  hori- 
zontal projection  of  the  point  A',  we  draw  a  perpen- 
dicular a  to  U  V,  the  ground  line,  this  perpendicular  a 
will  be  equal  to  the  measure  of  the  vertical  project- 
ant A'  A;  consequently,  the  distance  of  the  point  A' 
to  the  vertical  plane  is  equal  to  the  distance  between 
a,  its  horizontal  projection,  and  U  V,  the  ground  line 
measured  in  a  perpendicular  to  U  V.  In  like  man- 
ner, if  through  A,  the  vertical  projection  of  the  point 


A',  wc  draw  a  perpendicular  A  a  to  U  V,  the  ground 
line,  this  perpendicular  A  a  will  be  equal  to  the 
measure  of  the  horizontal  projectant  A  o;  conse- 
quently, the  distance  of  this  point  A'  to  the  horizon- 
tal plane  is  equal  to  the  distance  between  A,  its  ver- 
tical projection,  and  U  V,  the  ground  line  measured 
in  a  perpendicular  to  U  V. 

To  these  very  important  remarks  we  shall  add  one 
which  is  not  less  so.  Two  perpendiculars,  a  a,  Fig. 
6,  A  a,  being  let  fall  from  the  projections  a,  A  to  the 
same  point  A'  upon  the  ground  line  U  V,  will  meet 
each  other  in  the  same  point  a,  of  the  said  ground 
line  U  V. 

If  we  now  wished  the  two  projections  of  a  point 
A',  Fig.  6,  or  of  any  line  A'  B'  whatever,  to  be  upon 
one  or  the  same  plane,  it  is  sufficient  to  imagine  the 
vertical  plane  U  V  Y  Z  to  turn  round  the  ground 
line  U  V  in  such  a  manner  as  to  be  the  prolongation 
of  the  horizontal  plane  U  V  W  X;  for  it  is  clear  that 
this  plane  will  carry  with  it  the  vertical  projection  A 
or  A  B  of  the  point,  or  of  the  line  in  question.  More- 
over, we  see,  and  it  is  very  important,  that  the  lines 
A  a,  B  b,  perpendicular  to  the  ground  line  U  V,  will 
not  cease  to  be  so  in  the  motion  of  the  plane  U  V  Y 
Z ;  and  as  the  corresponding  lines  «  a,  i  b,  are  also 
perpendiculars  to  the  ground  line  U  V,  it  follows 
that  the  lines  a  a',  b  b',  will  be  the  respective  pro- 
longation of  the  lines  a  a,  i  b. 

Hence  it  results,  when  we  consider  objects  upon  a 
single  plane,  the  projections  a  A,  of  a  point  A'  in 
space,  are  necessarily  upon  the  same  perpendicular 
A  a  to  the  ground  line  U  Y. 

It  is  necessary  to  call  to  mind  that  the  distance 
A  a,  measures  the  distance  from  the  point  in  space  to 
the  horizontal  plane,  (the  point  A  being  the  vertical 
projection  of  this  point,)  and  that  the  line  a  a  meas- 
ures the  distance  from  the  same  point  in  space  to 
the  vertical  plane. 

It  follows,  that  if  the  point  in  space  be  upon  the 
horizontal  plane,  its  distance  with  regard  to  this  last- 
named  plane  will  be  zero  or  nothing,  and  the  vertical 
A  a  will  be  zero  also.  Moreover,  the  vertical  projection 
of  this  point  will  be  upon  the  ground  line  at  the  foot 
a,  of  the  perpendicular  a  a,  lot  fall  upon  the  ground 
line,  from  the  horizontal  projection  a  of  this  point. 

Again :  if  the  point  in  space  be  upon  the  vertical 
plane,  its  distance,  in  respect  of  this  plane,  will  be 
zero,  the  horizontal  a  a  will  be  zero,  and  the  hoiizon- 
tal  projection  of  the  point  in  question  will  be  the  foot 


PRACTICAL    GEOMETRY 


61 


a,  of  the  perpendicular  A  a,  let  fall  upon  the  ground 
line  from  the  vertical  projection  A,  of  this  point. 

In  general,  we  suppose  that  the  vertical  projection 
of  a  point  is  above  the  ground  line,  and  that  the 
horizontal  projection  is  below ;  but  from  what  has 
been  said,  it  is  evident  that,  if  the  point  in  space  be 
situated  below  the  horizontal  line,  its  vertical  projec- 
tion will  be  below  the  ground  line ;  for  the  distance 
from  this  point  to  the  horizontal  plane  cannot  be 
taken  from  the  base  line  to  the  top,  but  from  the  top 
to  the  base  with  respect  to  its  plane. 

So  if  the  point  in  space  be  situated  behind  the 
vertical  plane,  its  horizontal  projection  wUl  be  above 
the  ground  line;  from  which  we  conclude, — 

1.  K  the  point  in  question  be  situated  above  the 
horizontal  plane,  and  before  the  vertical  plane,  its 
vertical  projection  will  be  above,  and  its  horizontal 
projection  below,  the  ground  line. 

2.  If  the  point  be  situated  before  the  vertical  plane, 
and  below  the  horizontal  plane,  the  tw'o  projections 
will  be  above  the  ground  line. 

3.  K  the  point  be  situated  above  the  horizontal 
plane,  but  behind  the  vertical  plane,  the  two  projec- 
tions wiU  be  above  the  ground  line. 

.  4.  Lastly.  If  the  point  be  situated  above  the  hori- 
zontal plane,  and  behind  the  vertical  plane,  the  verti- 
cal projection  will  be  below,  and  the  horizontal  pro- 
jection above,  the  ground  line. 

The  reciprocals  of  these  propositions  are  also  true. 

If  a  line  be  parallel  to  one  of  these  planes  of  pro- 
jection, its  projection  upon  the  other  plane  will  be 
parallel  to  the  ground  line.  Thus,  for  example,  if  a 
line  be  parallel  to  a  horizontal  plane,  its  vertical  pro- 
jection will  be  parallel  to  the  ground  line ;  and  if  it  is 
parallel  to  the  vertical  plane,  its  horizontal  projection 
wiU  be  parallel  to  the  ground  line. 

Reciprocally,  if  one  of  the  projections  of  a  line  be 
parallel  to  the  ground  line,  this  line  will  be  parallel 
to  the  plane  of  the  other  projection.  Thus,  for  ex- 
ample, if  the  vertical  projection  of  a  line  be  parallel 
to  the  groimd  line,  this  line  will  be  parallel  to  the 
horizontal  plane,  and  vice  versa. 

If  a  line  be  at  any  time  parallel  to  the  two  planes 
of  projection,  the  two  projections  of  this  line  will  be 
parallel  to  the  ground  line ;  and  reciprocally,  if  the 
two  projections  of  a  line  be  parallel  to  the  ground 
line,  the  line  itself  will  be  at  the  same  time  parallel 
to  the  two  planes'  of  projection. 

K  a  line  be  perpendicular  to  one  of  the  planes  of 


projection,  its  projection  upon  this  plane  will  only  be 
a  point,  and  its  projection  upon  the  other  plane  will 
be  perpendicular  to  the  ground  line.  Thus,  for  ex- 
ample, if  the  line  in  question  be  perpendicular  to  the 
horizontal  plane,  its  horizontal  projection  wiU  be  only 
a  point,  and  its  vertical  projection  will  be  perpendic- 
ular to  the  ground  line. 

Reciprocally,  if  one  of  the  projections  of  a  straight 
line  be  a  point,  and  the  projection  of  the  other  per- 
pendicular to  the  ground  line,  this  line  will  be  per- 
pendicular to  the  plane  of  projection  upon  which  its 
projection  is  a  point.  Thus  the  line  will  be  perpen- 
dicular to  the  horizontal  plane,  if  its  projection  be 
the  given  point  in  the  horizontal  plane. 

K  a  line  be  perpendicular  to  the  ground  line,  the 
two  projections  will  also  be  perpendicular  to  this  line. 
The  reciprocal  is  not  true ;  that  is  to  say,  that  the 
two  projections  of  a  line  maybe  perpendicular  to  the 
ground  line,  without  having  the  same  line  perpendic- 
ular to  the  ground  line. 

K  a  line  be  situated  in  one  of  the  planes  of  pro- 
jection, its  projection  upon  the  other  will  be  upon  the 
grovmd  line.  Thus,  if  a  line  be  situated  upon  a  hori- 
zontal plane,  its  vertical  projection  will  be  upon  the 
ground  line ;  and  if  this  line  were  given  upon  the 
vertical  plane,  its  horizontal  projection  would  be  upon 
the  ground  line. 

Reciprocally,  if  one  of  the  projections  of  a  line  be 
upon  the  ground  line,  this  line  will  be  upon  the  plane 
of  the  other  projection.  Thus,  for  example,  if  it  be 
the  vertical  projection  of  the  line  in  question,  which 
is  upon  the  ground,  this  line  will  be  upon  the  hori- 
zontal plane ;  if,  on  the  contrary,  it  were  upon  the 
horizontal  projection  of  this  line  which  was  upon  the 
ground  line,  this  line  would  be  upon  the  vertical 
plane. 

If  a  line  be  at  any  time  upon  the  two  planes  of 
projcctioM,  the  tA.vo  projections  of  this  line  would  be 
upon  the  ground  line,  and  the  line  in  question  would 
coincide  with  this  ground  line.  Reciprocally,  if  the 
t^vo  projections  of  a  line  were  upon  the  ground  line, 
the  line  itself  would  be  upon  the  ground  line. 

If  two  lines  in  space  are  parallel,  their  projections 
upon  each  plane  of  projection  are  also  parallel.  Re- 
ciprocally, if  the  projections  of  two  lines  are  parallel 
on  each  plane  of  projection,  the  two  lines  will  be 
parallel  to  one  another  in  space. 

If  any  two  lines  whatever  in  space  cut  each  other, 
the  projections  of  their  point  of  intersection  will  be 


62 


PRACTICAL    GEOMETRY 


upon  the  same  perpendicular  line  to  the  ground  line, 
and  upon  the  points  of  intersection  of  the  projections 
of  these  lines.  Reciprocally,  if  the  projections  of 
any  two  lines  whatever  cut  each  other  in  the  two 
planes  of  projection  in  such  a  manner  that  their 
points  of  intersection  are  upon  the  same  perpendic- 
ular to  tlie  ground  line,  these  two  lines  in  question 
will  cut  each  other  in  space. 

The  position  of  a  plane  is  determined  in  space 
when  we  know  the  intersections  of  this  plane  with 
the  planes  of  projection. 

The  intersections  A  B,  A  C,  of  the  plane  in  ques- 
tion, witli  the  planes  of  projections,  arc  called  the 
traces  of  this  plane. 

The  trace  situated  in  the  horizontal  plane  is  called 
the  horizontal  trace,  and  the  trace  situated  in  the  ver- 
tical piano  is  called  the  vertical  trace. 

A  very  important  remark  is,  that  the  two  traces  of 
a  plane  intersect  each  other  upon  the  ground  line. 

If  a  plane  be  parallel  to  one  of  the  planes  of  pro- 
jection, this  plane  wiU  have  only  one  trace,  which 
will  be  paraDel  to  the  ground  line,  and  situated  in 
the  other  plane  of  projection.  Reciprocally,  if  a 
plane  has  a  trace  parallel  to  the  ground  line,  this 
plane  will  be  parallel  to  the  plane  of  projection, 
which  docs  not  contain  this  trace.     Thus  :  — 

1.  If  a  plane  be  parallel  to  the  horizontal  plane, 
this  plane  will  not  have  a  horizontal  trace,  and  its 
vertical  trace  will  be  parallel  to  the  ground  line. 
Likewise,  if  a  plane  be  parallel  to  the  vertical  plane, 
this  piano  will  not  have  a  vertical  trace,  and  its  hori- 
zontal trace  will  be  parallel  to  the  ground  line. 

2.  If  a  plane  has  only  one  trace,  and  this  ti-ace 
parallel  to  the  ground  line,  let  it  be  in  the  vertical 
plane ;  then  the  plane  will  be  parallel  to  the  horizon- 
tal plane.  So  if  the  trace  of  the  plane  be  in  the 
horizontal  plane,  and  parallel  to  the  ground  line,  the 
plane  will  be  parallel  to  the  vertical  plane.    . 

If  one  of  the  traces  of  a  plane  be  perpendicular  to 
the  ground  line,  and  the  other  trace  in  any  position 
whatever,  this  plane  will  be  perpendicular  to  the 
plane  of  projection  in  which  the  second  trace  is. 
Thus,  if  it  bo  a  horizontal  trace  which  is  perpendic- 
ular to  the  ground  line,  the  plane  will  be  perpendic- 
idar  to  the  vertical  plane  of  projection ;  and  if,  on 
the  contrary,  the  vortical  trace  be  that  which  is  per- 
pendicular to  the  ground  line,  tiien  the  plane  will  be 
perpendicular  to  the  horizontal  plane. 

Reciprocally,  if  a  plane  be  perpendicular  to  one  of 


the  planes  of  projection,  without  being  parallel  to  the 
other,  its  trace  upon  the  plane  of  projection,  to  which 
it  is  perpendicular,  will  be  perpendicular  to  any  posi- 
tion whatever,  and  the  other  trace  will  be  perpendic- 
ular to  the  ground  line.  Thus,  for  example,  if  the 
plane  be  perpendicular  to  the  vertical  plane,  the  ver- 
tical trace  will  be  perpendicular  to  the  ground  line. 
The  reverse  will  also  be  true,  if  the  plane  be  perpen- 
dicular to  the  horizontal  plane. 

If  a  plane  be  perpendicular  to  the  two  planes  of 
projection,  its  two  traces  will  be  perpendicular  to  the 
ground  line.  Reciprocally,  if  the  two  traces  of  a 
plane  are  in  the  same  straight  line  perpendicular  to 
the  ground  line,  this  plane  will  be  perpendicular  to 
both  the  planes  of  projection. 

If  the  two  traces  of  a  plane  are  parallel  to  the 
ground  line,  this  plane  will  be  also  parallel  to  the 
ground  line.  Reciprocally,  if  a  plane  be  parallel  to 
the  ground  line,  its  two  traces  will  be  parallel  to  the 
ground  line. 

When  a  plane  is  not  parallel  to  either  of  the  planes 
of  projection,  and  one  of  its  traces  is  parallel  to  the 
ground  line,  the  other  trace  is  also  necessarily  par- 
allel to  the  ground  line. 

If  two  planes  arc  parallel,  their  traces  in  each  of 
the  planes  of  projection  will  also  be  parallel.  Recip- 
rocally, if  on  each  plane  of  projection  the  traces  of 
the  two  planes  are  parallel,  the  planes  will  also  be 
parallel. 

If  a  line  be  perpendicular  to  a  plane,  the  projec- 
tions of  this  line  will  be  in  each  plane  of  projection 
perpendicular  to  the  respective  traces  in  this  plane. 
Reciprocally,  if  the  projections  of  a  line  are  respec- 
tively perpendicular  to  the  traces  of  a  plane,  the  line 
will  be  perpendicular  to  the  plane. 

If  a  line  be  situated  in  a  given  plane  by  its  traces, 
this  line  can  only  intersect  the  planes  of  projection 
upon  the  traces  of  the  plane  which  contains  it. 
Moreover,  the  line  in  question  can  only  meet  the 
plane  of  projection  in  its  own  projection.  Whence 
it  follows,  that  the  points  of  meeting  of  the  right 
line,  and  the  planes  of  projection,  arc  respectively 
upon  the  intersections  of  this  right  line,  and  the 
traces  of  the  plane  which  contains  it. 

K  a  right  line,  situated  in  a  given  plane  by  its 
ti-aces,  is  parallel  to  the  horizontal  plane,  its  horizon- 
tal projection  will  be  parallel  to  the  horizontal  trace 
of  the  given  plane,  and  its  vertical  projection  will  be 
parallel  to  the  ground  line.     Likewise,  if  the  right 


PRACTICAL    GEOMETRY. 


63 


line  situated  in  a  given  plane  by  its  traces  is  parallel 
to  the  vertical  plane,  its  vertical  projection  will  be 
parallel  to  the  vertical  line  of  the  plane  which  con- 
tains it,  and  its  horizontal  projection  will  be  parallel 
to  the  ground  line. 

Reciprocally,  if  a  line  be  situated  in  a  given  plane 
by  its  traces,  and,  for  example,  its  horizontal  pro- 
jection be  parallel  to  the  horizontal  trace  of  the 
given  plane,  this  line  will  be  parallel  to  the  horizon- 
tal plane,  and  its  vertical  projection  wiU  be  parallel 
to  the  ground  line.  Liliewise,  if  the  vertical  projec- 
tion of  the  line  in  question  be  parallel  to  the  vertical 
trace  of  the  given  plane,  this  line  will  be  parallel  to 
the  vertical  plane,  and  its  horizontal  projection  wiU 
be  parallel  to  the  ground  line. 


SECTION 

On  the  Developments  of  the  Surfaces  of  Solids. 

PROBLEMS. 
Plate  15. 

PROBLEM  I. 

To   find   tlie    development  of  the  surface  of  a 
right   semi-cylinder. 

Fig.  1.  Let  A  C  D  E  be  the  plane  passing  through 
the  axis.  On  A  C,  as  a  diameter,  describe  the  semi- 
circular arc  ABC.  Produce  C  A  to  B,  and  make 
A  F  equal  to  the  development  of  the  arc  ABC. 
Draw  F  G  parallel  to  A  E,  and  E  G  parallel  to 
A  F ;  then  A  F  G  E  is  the  development  required. 

PROBLEM  II. 

To  find  the  development  of  that  part  of  a  semi- 
cylinder  contained  between  two  perpendicular 
surfaces. 

Figs.  2,  3,  4.  Let  A  B  C  D  E  be  a  portion  of  a 
plane  passing  through  the  axis  of  the  cylinder,  C  D 
and  A  E  being  sections  of  the  surface,  and  let  D  E 
and  F  G  be  the  insisting  lines  of  the  perpendicular 
sTirface  ;  also,  let  A  C  be  perpendicular  to  A  E  and 
C  D.  On  A  C,  as  a  diameter,  describe  the  semicir- 
cular arc  ABC.  Produce  C  A  to  H,  and  make 
A  H  equal  to  the  development  of  the  arc  ABC. 
Divide  the  arc  ABC  and   its  development  each 


into  the  same  number  of  equal  parts,  at  the  points 
1,  2,  3. 

Though  the  points  1,  2,  3,  &c.,  in  the  semicircular 
arc,  and  in  its  development,  draw  straight  lines  par- 
allel to  A  E,  and  let  the  parallel  lines  through  1,  2,  3, 
in  the  arc  ABC,  meet  F  G  in  p,  rj,  r,  Sec,  and  A  C 
in  k,  I,  m,  &c.  Transfer  the  distances  Icp,  Iq,  vir,  &c., 
to  the  development  upon  the  lines  1  a,2  b,3  c,  &c. 
Through  the  points  F,  a,  b,  c,  &c.,  draw  the  curve 
line  F  c  1.  In  the  same  manner  draw  the  curve  line 
E  K ;  then  F  E  I  K  will  be  the  development  re- 
quired. 

PROBLEM  III. 

To  find  the  development  of  the  half  surface  of 
a  right  cone,  terminated  by  a  plane  passing 
through  the  axis. 

Fig.  5.  Let  A  C  E  be  the  section  of  the  cone  pass- 
ing along  the  axis  A  E,  and  C  E  the  straight  lines 
which  terminate  the  conic  surface,  or  the  two  lines 
which  are  common  to  the  section  C  A  E  and  the 
conic  surface ;  and  let  A  C  be  the  line  of  common 
section  of  the  axal  plane  and  the  base  of  the  cone. 

On  A  C,  as  a  diameter,  describe  a  semicircle, 
ABC.  From  E,  with  the  radius  E  A,  describe  the 
arc  A  F,  and  make  the  arc  A  F  equal  to  the  semi- 
circular arc  ABC,  and  join  E  F;  then  the  sector 
A  E  F  is  the  development  of  the  portion  of  the 
conic  surface  required. 

PROBLEM  IV. 

To  find  the  development  of  that  portion  of  a 
conic  surface  contained  by  a  plane  passing 
along  the  axes,  and  two  surfaces  perpendic- 
ular to  that  plane. 

Fig.  6.  Let  A  C  E  be  the  section  of  the  cone 
along  the  axis,  and  let  A  C  and  G  I  be  the  insisting 
lines  of  the  perpendicular  surfaces.  Find  the  devel- 
opment A  E  F,  as  in  the  preceding  problem.  Divide 
the  semicircular  arc  ABC,  and  the  sectorial  arc 
A  F,  each  into  the  same  number  of  equal  parts  at 
the  points  1, 2,  3,  &c.  From  the  points  1,  2,  3,  &c., 
in  the  semicircular  arc,  draw  straight  Lines,  1  k,  2  /, 
3  m,  &c.,  perpendicular  to  A  C.  From  the  points 
k,  I,  m,  &c.,  draw  straight  lines,  A;  E,  Z  E,  m  E,  Sec, 
intersecting  the  curve  A  C  in  j?,  q,  r,  &c.  Draw  the 
straight  lines  pt,  qu,  rv,  &cc,  parallel  to  one  side,  E  C 
meeting  A  C  in  the  points  t,  u,  v,  Sec    Also  from  the 


64 


PROJECTION    OF    PRISMS. 


points  1,  2,  3,  in  the  sectorial  arc  A  F,  draw  the 
straight  lines  1  E,  2  E,  3  E,  &c.  Transfer  the  dis- 
tances pt,  qii,  rv,  &c.,  to  1  a,  2  b,  3  c,  &cc. ;  then, 
through  the  points  A,  a,  b,  c,  &c.,  draw  the  curve 
A  c  F,  and  A  c  F  is  one  of  tlie  edges  of  the  develop- 
ment, and  by  drawing  the  other  edge,  the  entire  de- 
velopment, A  G  H,  will  be  found. 

Note.  —  This  treatise    on    the  subject  of  Geometry  we  have 
thought  best  to  insert  in  the  form  in  which  it  was  fiist  written.    It 


is  a  system  in  a  degree  peculiar  to  its  author,  and  it  is,  without 
doubt,  the  production  of  a  laborious  research ;  and  although  the 
same  conclusions  would,  in  some  cases,  be  arrived  at  by  the  more 
direct  process  of  demonstration  used  at  the  present  day,  yet,  from  its 
extent  and  completeness,  we  have  concluded,  as  a  whole,  that  no 
part  could  be  materially  changed  for  the  better  without  seriously 
intruding  upon  the  theories  of  our  venerable  author,  and  that,  too, 
at  the  expense  of  interfering  with  liis  style  of  writing,  wliich  will 
at  once  be  recognized  as  the  original.  We  will  state  here,  that  we 
have  endeavored,  as  much  as  possible,  to  preserve  every  idea  that 
he  has  advanced,  and  that,  toO;  in  his  own  language.  —  Editors. 


PROJECTION   or    PRISMS. 


In  the  annexed  definitions  and  problems,  the  student  will  find 
enough  to  give  him  a  correct  and  sufficiently  perfect  idea  of  the 
nature  and  importance  of  this  useful  branch  of  science ;  and  he 
will  also  find  occasion  to  apply  the  geometrical  principles,  a  knowl- 
edge of  which  he  is  presumed  to  have  acquired  from  the  preceding 
pages  of  the  present  work. 


DEFINITIONS. 

1.  When  straight  lines  are  drawn  according  to  a 
certain  law  from  the  several  parts  of  any  figure  or 
object  cut  by  a  plane,  and  by  that  cutting  or  inter- 
section describe  a  figure  on  that  plane,  the  figure  so 
described  is  called  the  projection  of  the  other  figure 
or  object. 

2.  The  lines  taken  altogether,  which  produce  the 
projection  of  the  figure,  are  called  a  syatem  of  rays. 

3.  When  the  system  of  rays  are  all  parallel  to 
each  other,  and  are  cut  by  a  plane  perpendicular  to 
them,  the  projection  on  the  plane  is  called  the  orlhog- 
raphy  of  the  figure  proposed. 

4.  When  the  system  of  parallel  rays  is  perpendic- 
ular to  the  horizon,  and  projected  on  a  plane  parallel 
to  the  horizon,  the  orthographical  projection  is  then 
called  the  ichnography,  or  plan  of  the  figure  proposed. 

5.  When  the  rays  of  the  system  are  parallel  to 
each  other  and  to  the  horizon,  and  if  the  projection 
be  made  on  a  plane  perpendicular  to  those  rays  and 
to  th(!  horizon,  it  is  called  the  elevation  of  the  figure 
proposed. 

[In  this  kind  of  projections,  the  projection  of  any 
particular  point  or  line  is  sometimes  called  the  seat 
of  that  point  or  line,  on  the  plane  of  projection.] 

G.  If   a   solid   be   cut  by  a  plane   passing  quite 


through  it,  the  figure  of  that  part  of  the  solid  which 
is  cut  by  the  plane  is  called  a  section. 

7.  When  any  solid  is  projected  orthographieally 
upon  a  plane,  the  outline  or  boundary  of  the  projec- 
tion is  called  the  contour  or  profile  of  the  projection. 

Note.  —  Although  the  term  orthography  signifies,  in  general,  the 
projection  of  any  plane  which  is  perpendicular  to  the  projecting 
rays,  without  regarding  the  position  of  the  plane  on  which  the  ob- 
ject is  projected,  yet  writers  on  projection  substitute  it  for  elevation, 
as  already  defined,  by  which  means  it  will  be  impossible  to  know 
when  we  mean  that  particular  position  of  orthographical  projection 
which  is  made  on  a  plane  perpendicular  to  the  hori/on. 

Axiom.  —  K  any  point,  line,  or  plane  of  any  origi- 
nal figure  or  object  touch  the  plane  on  which  it  is 
to  be  projected,  the  place  where  it  touches  the  pro- 
jecting plane  is  the  projection  of  that  point,  line,  or 
plane  of  the  original  figure  or  object. 

Proposition.  —  The  orthographical  projection  of  a 
line  which  is  parallel  to  the  plane  of  projection  is  a 
line  equal  and  parallel  to  its  original. 

PROBLEMS. 

Plate   16. 

PROBLEM    I. 

To  project  the  elevation  of  a  prism  standing  on 

a  plane  perpendicular  to  the  projecting  plane ; 

giA'en,  the  base  of  the  prism  and  its  position 

to  the  projecting  plane. 

Fig.  1.  Let  A  B  C  D,  No.  1,  be  the  base  of  the 
prism ;  let  H  F  be  the  intersection  of  the  projecting 
plane,  with  the  plane  on  which  the  prism  stands. 

Draw  lines  from  every  angle  of  the  base,  cutting 


T  K 


fw  /.]■■■/ 


PEOJECTION    OF    PRISMS. 


65 


H  F  at  H,  and  F  will  be  the  projection  of  the  points 
A  and  C ;  the  angle  D,  touching  H  F  at  D,  is  its 
projection. 

From  each  of  the  points  H,  D,  F,  in  No.  2,  draw 
the  lines  H  I,  D  E,  and  F  G,  each  perpendiciilar  to 
H  F ;  make  D  E  eqnal  to  the  height  of  the  prism ; 
through  E  di'aw  I  G,  cutting  H  I  and  F  G  at  I  and 
G,  which  will  give  the  projection  sought. 

PROBLEM    II. 

To  project  the  ichnograpliy  and  elevation  of  a 
square  prism,  to  rest  upon  one  of  its  angles 
upon  a  given  point  A,  in  the  plane,  on  which 
tlie  ichnography  is  to  be  described ;  given  the 
ichnograpliy  A  L,  of  an  angle,  wliich  the  two 
under  planes  make  with  each  other;  the 
angle  ]\I  a  I,  which  the  angle  of  the  solid 
makes  with  its  ichnography  A  L ;  the  inter- 
section A  a  of  one  of  its  ends  with  the  plane 
of  the  ichnography  ;  the  angle  D  A  «,  which 
one  side  of  the  end  makes  at  A,  with  the  in- 
tersection A  a  of  that  end ;  also  given  one  of 
the  sides  of  the  ends,  and  the  length  of  the 
prism. 

Fig.  2.  At  the  given  point  A,  with  the  intersection 
A  a,  make  an  angle  a  AT>,  equal  to  the  angle  which 
one  of  the  sides  of  the  end  makes  with  A  a;  make 
A  D  equal  to  one  of  the  sides  of  the  end;  then  on 
A  D  consti-uct  the  square  A  B  C  D ;  through  the 
angles  of  the  square  B,  C,  D,  draw  lines  B  H,  C  I, 
and  D  M,  parallel  to  A  L ;  then  at  the  point  a,  in 
the  right  line  D  M,  make  an  angle  M  a  1,  with  a  M, 
equal  to  the  angle  of  the  solid,  whose  projection  is 
A  L,  with  A  L ;  make  a  I  equal  to  the  length  of  the 

9 


solid  ;  through  the  points  a  and  /,  No.  1,  draw  the  lines 
a  e  and  I  i  perpendicular  to  a  I ;  through  the  points 
B  and  C,  No.  2,  draw  B  R  and  C  S  parallel  to  A  a, 
cutting  D  M,  produced  at  E,  and  S ;  on  a,  as  a  cen- 
tre, with  the  distances  a  D,  a  R,  and  a  S,  describe 
ares  V  g,  R/,  and  S  e,  cutting  a  e,  No.  1,  at  g-,  /,  e  ; 
through  the  points  g,  f,  e,  draw  the  lines  g-  k,  f  h, 
and  e  i,  parallel  to  a  I,  and  No.  1  will  be  completed, 
which  will  be  the  projection  of  tlie  prism  on  a  plane 
parallel  to  A  L.  Through  the  points  g,  f,  e,  draw 
the  lines  e  E,  /  F,  and  g  G,  perpendicular  to  D  M, 
or  A  L,  cutting  D  E,  C  I,  and  B  H,  respectively,  at 
G,  E,  F;  also  through  the  points  I,  k,  h,  i,  cbaw  the 
lines  I  L,  k  K,  h  H,  and  i  I,  Hkewise  parallel  to  A  L, 
cutting  A  L,  G  M,  B  H,  and  C  I,  respectively,  at  the 
points  L,  K,  H,  and  I ;  join  E  F,  E  G,  and  H  I, 
I  K,  K  L,  L  H,  then  will  the  planes  E  F  H  I, 
E  I  K  L,  and  H  I  K  L  represent  the  ichnogi-aphy 
of  the  upper  sides  of  the  solid  ;  and  if  F  A  and  A  G 
be  joined,  then  will  F  A  G  E,  F  A  L  H,  and  G  A 
L  K  represent  the  sides  of  the  solid  next  to  the 
plane  of  projection.  Then  to  project  the  elevation 
on  a  plane  whose  intersection  is  T  U,  from  F,  E,  G, 
A,  H,  I,  K,  and  L,  that  is,  from  all  the  points  in  the 
ichnography  representing  the  solid  angles,  di-aw  the 
lines  F  /,  E  e,  G^,  A  o,  H  h,  I  i,  K  k,  and  L  I,  per- 
pendicular to  the  intersection  T  U,  cutting  T  U  at 
P>  5')  (^>  §">  o,  m,  and  k ;  make  p  f^  q  e,  g  g,n  h,  o  i, 
m  I,  and  k  k,  at  No.  3,  respectively,  equal  to  P/,  Q  e, 
G  g-,  N  A,  O  i,  M  I,  and  K  k,  at  No.  1 ;  then  join 
f  a,  a  g,  g  e,  e  f;  e  i,  i  k,  k  g,  k  I,  and  la;  and 
fage,  geik,  gkla  will  be  the  elevations  of  the 
outside  planes  of  the  solid;  and  by  joining/ A,  and 
h  i,fh  i  e,fh  I  a,  and  i  h  I  k  will  be  the  elevations 
of  the  planes  of  the  solid  next  to  the  plane  on  which 
the  elevation  is  projected. 


66 


SHADOWS 


SHADOWS. 


This' is  one  of  the  most  interesting  branches  of  architectural  sci- 
ence I  or  perhaps  it  may,  with  more  propriety,  be  termed  a  branch 
of  geometry,  for  it  is  almost  entirely  dcpenilent  on,  and  governed 
by,  geometrical  principles. 

From  a  knowledge  of  it  the  architect  is  enabled  to  draught  his  plans, 
and  to  give  them  their  true  effect,  or  representation  of  light  and 
shade ;  to  construct  his  windows  in  order  to  receive  light  to  the  best 
advantage,  &c.,  &c.  The  art  of  keeping  a  proper  gradation  of  light 
and  shade  on  objects,  according  to  their  several  distances,  colors, 
and  other  circumstances,  is  of  the  utmost  consequence  to  the  artist. 


THE  EFFECT    OF   DISTANCE   ON   THE 
'  COLOR   OF   OBJECTS. 

The  art  of  giving  a  due  diminution  or  degradation 
to  the  strength  of  the  light  and  shade  and  colors  of 
objects,  according  to  the  different  distances,  the  quan- 
tity of  light  which  falls  on  their  surfaces,  and  the 
medium  through  which  they  are  seen,  is  called 
keeping;. 

1.  When  objects  are  removed  to  a  gi-cat  distance 
from  the  eye,  the  rays-  of  light  Avhicli  they  reflect 
will  be  less  vivid,  and  the  color  will  become  more 
diluted,  and  tinged  wiih  a  faint  bluish  cast,  by  rea- 
son of  the  great  body  of  air  through  which  they  are 
seen. 

2.  In  general,  the  shadows  of  objects,  according  as 
they  are  more  remote  from  Hie  eye,  will  be  lighter, 
and  the  light  parts  will  become  darker ;  and  at  a 
certain  distance  the  light  and  shadow  are  not  distin- 
guishable from  each  other,  for  both  will  seem  to  ter- 
minate in  a  bluish  lint  of  the  color  of  the  atmosphere, 
and  will  appear  entirely  lost  in  that  color. 

3.  If  the  rays  of  light  fall  upon  any  colored  sub- 
stance, the  reflected  rays  will  be  tinged  with  the  color 
of  that  substance. 

4.  If  the  colored  rays  be  reflected  upon  any  object, 
the  color  of  that  object  will  then  be  compounded 
of  the  color  of  the  reflected  rays  and  the  color 
of  the  object ;  so  that  the  color  of  the  object  which 
receives  the  reflection  will  be  changed  into  another 
color. 

5.  From  the  closeness  or  openness  of  tlie  place 
where  the  object  is  situated,  the  light,  being  much 


more  variously  directed,  as  in  objects  which  are  sur- 
romidcd  by  buildings,  will  be  more  deprived  of  re- 
flection, and,  consequently,  will  be  darker  than  those 
which  have  no  other  objects  in  their  vicinity,  except 
the  surrounding  objects  are  so  disposed  as  to  reflect 
the  rays  of  light  upon  them. 

6.  In  a  room,  the  light  being  more  variously  di- 
rected and  reflected  than  abroad  in  the  open  air,  (for 
every  apertm-e  gives  an  inlet  to  a  different  stream,) 
which  direction  is  various,  according  to  the  place  and 
position  of  the  apertm-e,  whereby  every  diflcrent  side 
of  the  room,  and  even  the  same  side  in  such  a  situa- 
tion, will  be  variously  afTected  with  respect  to  their 
light,  shade,  and  colors,  from  what  they  would  in  an 
open  place  when  exposed  to  rays  coming  in  the  same 
direction. 

Some  original  colors  naturally  reflect  light  in  a 
greater  proportion  than  others,  though  equally  ex- 
posed to  the  same  degrees  of  it,  whereby  their  degra- 
dation at  different  distances  will  be  different  from 
that  of  other  colors  which  reflect  less  light. 

The  art  of  keeping  a  degradation  of  light  and  shade 
on  objects,  according  to  their  several  distances,  colors, 
and  other  circumstances,  is  of  the  utmost  conse- 
quence to  the  artist. 

In  orthographical  projections,  where  equal  and 
similar  objects  stand  in  the  same  position  to  the 
plane  of  projection,  they  will  be  represented  similar, 
and  of  an  equal  magnitude  at  every  distance  from 
that  plane  ;  and,  consequently,  planes  wliich  are  par- 
allel to  each  other  would  not  appear  to  have  any  dis- 
tance, so  that  the  representation  of  any  number  of 
objects,  at  different  distances  from  each  other,  would 
be  entirely  confused,  and  no  particular  object  could 
be  distinguished  from  the  others ;  but,  by  a  proper 
attention  to  the  art  of  kccpitig;,  every  object  will  be 
distinct  and  separate,  and  their  respective  distances 
and  colors  from  each  other  will  be  preserved.  But 
though  a  proper  degradation  of  light  and  shade  ought 
to  be  preserved,  according  to  the  respective  distances 
of  objects  from  each  other,  artists  in  general  take  too 
gi"cat  liberties  with  nature  :  we  frequently  see  in  the 
drawings  of  architects  the  art  of  keeping  carried  to 
so  great  an  extreme  as  to  render  their  performances 
ridiculous. 


SHADOWS. 


67 


DEFINITIONS. 

1.  A  body  which  is  continually  emitting  a  stream 
of  matter  from  itself,  and  thereby  rendering  objects 
visible  to  our  sense  of  seeing,  is  called  a  luminary; 
such  as  the  sun,  or  any  other  body  producing  the 
same  effect. 

2.  The  stream  of  matter  which  is  emitted  from  the 
luminary  is  called  light. 

3.  A  substance  or  body  which  light  cannot  pene- 
trate is  called  an  opaque  hodij. 

4.  If  a  space  be  deprived  of  light  by  an  opaque 
body,  it  is  called  a  shade. 

5.  The  whole  or  part  of  any  sm-face  on  which  a 
shade  is  projected  is  called  a  shadow. 

6.  A  body  which  will  admit  of  light  to  pass  through 
it  is  called  a  transparent  substance. 

7.  A  line  of  light  emitted  from  the  luminary  is 
called  a  ray. 

Proposition  1.  —  The  rays  of  light,  after  issuing 
from  the  luminary,  proceed  in  straight  lines. 

Proposition  2.  —  If  the  rays  of  light  fall  upon  a  re- 
flectiiig  plane,  the  angle  made  by  any  incident  ray, 
and  a  perpendicular  to  the  reflecting  plane,  is  called 
the  angle  of  incidence,  and  ■wHl  be  equal  to  the  angle 
that  its  reflected  ray  will  make  with  the  same  per- 
pendicular, called  the  angle  of  reflection ;  these  two 
propositions  are  known  lirom  experiment. 

Proposition  3.  —  If  the  rays  of  light  fall  upon  any 
curved  surface,  whether  concave  or  convex,  or  mLxed 
of  the  tvs^o,  the  angle  of  reflection  will  stiU  be  equal 
to  the  angle  of  incidence. 

Proposition  4.  —  Any  uneven  reflecting  surface, 
whose  parts  lie  in  various  directions,  will  reflect  the 
rays  of  the  sun  in  as  many  different  directions. 

Demonstration.  —  If  any  ray  fall  upon  a  part  of 
the  surface  which  is  perpendicular  to  that  ray,  it  will 
be  reflected  m  the  same  line  as  the  incident  ray ;  but 
the  more  or  less  any  part  of  the  surface  is  inclmed  to 
a  ray,  falling  upon  that  part  of  the  surface,  the  greater 
or  less  angle  will  the  reflected  ray  make  with  the  in- 
cident ray.  For  imagine  a  perpendicular  to  be  erected 
to  that  part  of  the  surface  where  any  incident  ray 
impinges  on  the  surface,  it  is  evident  that  the  meas- 
ure of  the  angle  of  incidence  is  equal  to  the  obtuse 
angle  made  by  the  incident  ray,  and  the  reflecting 
surface  at  the  impinging  point  made  less  by  a  right 
angle ;  but  the  angle  of  reflection  is  equal  to  the  an- 
gle of  incidence ;  wherefore  it  follows  that  the  whole 


angle  formed  by  the  incident  and  reflected  rays  is 
double  of  the  angle  of  incidence ;  and,  consequently, 
a  reflecting  surface,  whose  parts  lie  in  various  direc- 
tions, wiU  reflect  the  sun's  rays  in  as  many  directions. 
Corollary.  —  Hence  appears  the  reason  why  objects 
and  their  parts  become  visible  to  our  sight  when  im- 
mersed ui  shade. 


SEAT    OF    THE    SUN'S    RAYS. 

DEFINITIONS. 

1.  If  a  given  straight  line  pass  through  or  cut  a 
given  plane,  and  if  an  imaginary  plane  be  supposed 
to  pass  through  any  two  points  m  the  straight  Ihie, 
perpendicular  to  the  other  plane,  the  angle  made  by 
the  intersection  of  the  two  planes  and  the  given 
straight  line  is  called  the  inclination  or  altitude  of 
the  given  line  on  the  given  plane. 

2.  The  intersection  of  the  planes  is  called  the  seat 
of  the  given  line  on  the  given  plane. 

Corollary.  —  The  angle  made  by  a  ray  of  light, 
and  the  seat  of  that  ray,  is  the  angle  of  the  sun's  in 
clination. 

3.  If  on  the  surface  of  any  solid  there  be  any  point 
or  points  in  the  surface  where  the  sun's  rays  fall  per- 
pendicular, this  point  or  points  which  the  sun's  rays 
fall  perpendicular  to  are  called  points  of  light. 

4.  If  on  the  sm-face  of  any  solid  there  be  any  Ime 
drawn  upon  that  surface,  and  if  the  line  so  drawn 
upon  the  surface  be  lighter  than  any  other  line  that 
can  be  drawn  upon  the  said  surface,  then  the  line  first 
drawn  is  called  the  line  of  light. 

5.  K  the  sun's  rays  fall  upon  any  solid,  and  if  a 
line  or  lines  be  drawn  on  the  surface  of  the  solid 
where  the  sun's  rays  are  a  tangent,  or  upon  the  place 
or  places  of  the  surface  which  divide  the  dark  side 
from  the  light  side,  then  the  line  or  lines  so  described 
are  caUed  a  line  or  lines  of  shade. 

6.  If  the  sun's  rays  be  parallel  to  any  plane,  that 
plane  to  which  they  are  parallel  is  called  a  plane  of 
shade. 

PROBLEiAIS. 

PROBLEM  I. 

Given  the  ichnography  aud  elevation  of  a  prism, 
whose  sides  stand  perpenchcular  to  the  hori- 
zon, and  whose  ichnography  is  a  figure  of 


68 


SHADOWS. 


an)  kind,  regular  or  irregular ;  given  the  scat 
of  the  sun  on  the  ichnography,  also  on  the 
elevation,  and  the  intersection  of  the  plane 
of  the  elevation  with  the  plane  of  the  ichnog- 
raphy; the  representation  of  the  point  being 
likewise  given  on  the  elevation,  and  also  on 
the  ichnography,  to  determine  the  representa- 
tion of  the  shadow  on  the  elevation. 

Through  the  representation  of  the  given  point  in 
the  plane  of  tlie  ichnography  ckaw  a  line  parallel  to 
the  scat  of  the  sun's  rays  on  that  plane,  and  produce 
it  till  it  cut  the  intersection  ;  from  that  point  on  the 
elevation  draw  a  line  perpendicular  to  the  intersec- 
tion ;  then  through  the  representation  of  the  given 
point  on  the  elevation  draw  a  line  parallel  to  the  sun's 
seat  on  the  elevation,  cutting  the  line  that  was  di-awn 
perpendicular  to  the  intersection,  and  that  point  will 
be  the  representation  of  the  shadow  on  the  elevation. 

Plate  17. 

PROBLEM  11. 

Given  the  altitude  and  seat  of  the  sun  on  the 
horizon  and  the  intersection  of  a  plane,  mak- 
ing a  given  angle  with  the  horizon ;  to  find 
the  seat  and  altitude  of  the  sun  on  the  other 
plane. 

Fig.  1.  Let  D  F  be  the  seat  of  the  sun  on  the 
horizon,  and  D  F  G  the  angle  of  the  sun's  elevation, 
E  F  the  intersection  of  the  plane  with  the  horizon, 
and  ABC  the  angle  which  that  plane  is  to  make 
with  the  horizon. 

Produce  D  F  till  it  meet  E  F  in  F ;  through  any 
point  D,  in  the  seat  D  F,  draw  D  G  perpendicular  to 
D  F,  cutting  F  G  in  G ;  also,  through  D  draw  D  K 
perpendicular  to  E  F,  cutting  E  F  in  E ;  through  D 
draw  D  I  perpendicular  to  D  K;  make  the  angle 
D  E  11  equal  to  the  given  angle  ABC;  make  D  I 
equal  to  D  G ;  through  I  draw  I  H  perpendicular  to 
E  H,  cutting  it  in  II;  make  E  K  equal  to  E  II;  join 
K  F ;  fi'om  K  make  K  L  perpendicular  to  K  F ;  from 
K  make  K  L  equal  to  H  I ;  join  L  F ;  then  will  I  K 
be  the  scat  of  the  sun  on  the  other  plane,  and  K  F  L 
will  be  the  angle  of  the  altitude. 

If  the  plane  KEF  stands  perpendicular  to  the 
horizon,  as  m  Fig.  2,  the  operation  will  be  more  sim- 


ple, as  follows,  the  same  letters  standing  for  the  same 
things :  — 

Make  E  K  equal  to  D  G ;  join  K  F ;  draw  K  L, 
as  before,  and  make  K  L  equal  to  D  E ;  join  L  F ; 
then  will  K  F  be  the  seat  of  the  sun  on  the  horizon, 
and  K  F  L  be  the  seat  of  the  altitude. 

Plate  18. 

PROBLEM  UI. 

Given  the  ichnography  A  B  C  D  E  F  G  H  I  K, 
and  elevation  L  M  N  O,  of  an  upright  prism, 
whose  base  or  ichnography  is  a  regular  poly- 
gon, and  the  seat  of  the  sun's  rays  on  the  base, 
to  determine  the  various  degrees  of  light  and 
shade  on  the  different  sides  of  the  prism. 

Fig.  1.  Let  P  Q,  in  the  ichnography,  be  the  seat 
of  the  sun ;  and  if  it  cut  C  D  perpendicular,  then  will 
C  D  be  the  lightest  side  of  the  prism  ;  the  sides  D  E 
and  C  B  will  be  a  small  degree  darker,  as  P  Q  is 
more  inclined  to  D  E  and  C  B ;  and  in  general,  ac- 
cording as  the  sides  recede  on  each  side  of  C  D,  they 
wiU  be  contintially  darker  untU  they  become  wholly 
deprived  of  light ;  then  suppose  the  sun's  ray  to  touch 
the  side  G  H,  then  G  H  -will  be  the  plane  of  shade, 
or  that  side  where  the  light  wiU  end. 

Much  in  the  same  manner  may  the  different  de- 
grees of  shade  be  found  on  the  surface  of  a  cylinder, 
as  in  Fig.  2,  where  A  B  C  D  is  the  ichnogi-aphy,  and 
G  H  I  K  the  elevation ;  that  is,  if  B  P  be  the  direc- 
tion of  the  sun's  rays,  cutting  the  ichnogi-aphy  in  B. 
then  will  B  be  the  lightest  place  ;  and  it  will  be  con- 
tinually darker  and  darker  in  each  side  of  the  pomt 
B,  until  it  arrives  at  the  point  C,  where  the  ray 
touches  the  side  of  the  cylinder,  and  there  the  light 
will  end  and  the  darkness  begin. 

PROBLEM  IV. 

To  represent  the  boundaries  of  light  and  shade 
on  the  ele^■ation  of  a  cone  illumined  by  the 
sun,  given  the  angle  that  any  ray  of  light  takes 
with  the  base  of  the  cone ;  also  to  determine 
the  line  of  light,  or  that  place  on  the  surface 
that  will  be  the  lightest. 

Figs.  3  and  4.  Let  A  E  D  be  the  elevation  of  the 
cone,  and  let  F  I  L  G  be  the  ichnography  or  base  of 
the  cone  ;  let  F  L  be  the  seat  of  any  ray  in  a  plane 


II  17 


,111 


«!ll'J<?\'i.'i(:)'5 


K       M 


O  I 


J^t^^sT      IB 


ri.m 


SHADOWS, 


69 


passing  through  the  axis,  and  let  the  angles  M  L  F, 
Fig.  3,  and  L  F  M,  Fig.  4,  be  the  angles  which  a  ray 
of  light  makes  with  the  base  of  the  cone,  and  let 
F  N  L  be  a  section  of  the  cone  passing  through  the 
axis,  and  through  F  L;  consequently,  the  rays  M  L 
and  F  ]\I  will  be  in  that  plane. 

Produce  the  rays  M  L  and  F  M,  if  necessary,  until 
they  cut  the  sides  of  the  section  N  F  and  N  L; 
Fig.  3  will  be  cut  at  the  points  M  and  L,  and  Fig.  4 
at  the  points  F  and  M :  bisect  each  of  the  lines  M  L 
and  F  M ;  and  through  N,  the  vertex  of  the  cone, 
and  the  point  of  bisection,  draw  N  K ;  through  K 
draw  I  K  G,  at  right  angles  to  F  L ;  through  the 
points  G  and  F  di-aw  the  lines  G  C  and  F  B  per- 
pendicular to  A  D,  the  representation  of  the  base, 
cutting  A  D  at  B,  and  C  in  the  elevation,  and  join 
B  E  and  C  E ;  then  will  B  E  be  the  lightest  line  that 
can  be  di-awn  on  the  sm-face  of  the  cone,  and  C  E 
will  be  the  representation  of  a  line  which  will  divide 
the  light  side  of  the  cone  from  the  dark  side,  and 
B  E  C  will  be  the  representation  of  half  the  enlight- 
ened side  of  the  cone. 

Plate   19. 

PROBLEM  V. 

Given  the  iclinography  and  elevation  of  a  polyg- 
onal ring,  or  a  ring  made  of  cylinders  of 
equal  lengths,  and  making  equal  angles  with 
each  other,  to  determine  the  representation 
of  the  boundaries  of  light  and  shade  on  the 
ichnography  and  elevation ;  the  sun's  altitude 
and  seat  to  the  plane  on  which  the  ichnog- 
raphy is  described  being  given. 

Let  A  C  be  the  seat  of  the  sun  in  the  plane  of  the 
ichnography,  cutting  the  thickness  of  the  ring  at  A 
and  B ;  let  A  C  D  be  the  angle  which  the  sun's  rays 
make  with  the  plane  of  the  ichnogi'aphy,  or  seat  A  C. 

Bisect  A  B  in  c;  with  the  radius  c  A  or  c  B  de- 
scribe a  circle ;  and  through  the  centre  c  draw  c  d 
parallel  to  C  D,  cutting  the  circle  at  d;  also  through 
c  ch-aw  the  line  a  6  at  right  angle  to  c  d,  cutting  the 
circles  at  a  and  b ;  through  the  points  d  and  b  draw 
lines  parallel  tc  the  sides  A  and  B  of  the  ring ;  then 
the  dark  line  nearest  to  A  will  represent  the  line  of 
light ;  and  that  which  is  nearest  to  B  will  represent 
that  line  which  separates  the  light  side  from  the 
dark  side. 


To  find  the  lines  of  light  and  shade  on  the  next 
side  of  the  ichnography:  from  the  centre  C  draw 
C  E  at  right  angles  to  the  side  E,  cutting  the  sides 
E  and  F  at  E  and  F ;  through  the  point  A  draw 
H  A  G  at  right  angles  to  E  C,  cutting  E  C  at  G ; 
from  G  make  G  II  equal  to  A  D,  join  H  C,  and 
bisect  E  F  at  c ;  then  with  the  radius  c  E  on  c  F 
describe  a  circle,  and  through  its  centre  e,  draw  c  k 
parallel  to  C  H,  cutting  the  circle  at  k;  also  through 
c  draw  p  f  at  right  angles  to  c  k ;  through  the  points 
k  and/,  draw  lines  parallel  to  the  sides  E  and  F  ; 
then  will  the  line  next  to  E,  that  cuts  C  F  at  ^,  be 
the  line  of  light,  and  the  line  next  to  F  the  line  of 
sliade. 

In  like  manner  proceed  with  the  side  I  and  K;  that 
is,  through  C  draw  the  line  CI  at  right  angles  to  the 
side  I,  cutting  the  sides  I  and  K  at  I  and  K ;  bisect 
I  K  at  c  ;  with  the  radius  c  I  or  c  K  describe  a  circle  ; 
through  the  point  A,  as  before,  di-aw  the  line  A  L 
perpendicular  to  C  I,  cutting  C  I  at  L ;  from  L,  make 
L  M  equal  to  A  D ;  join  M  C ;  through  c  draw  c  m 
parallel  to  C  M,  cutting  the  circle  at  m ;  also  through 
c  draw  g  h  perpendicular  to  c  m,  cutting  the  circle  at 
g  and  h;  then  through  the  points  m  and  h  draw  lines 
parallel  to  the  sides  I  and  K ;  then  the  line  next  to  I, 
which  cuts  I  K  at  s,  will  give  the  line  of  light,  and 
the  line  next  to  K  the  line  of  shade. 

In  like  manner,  to  find  the  common  boundary  of 
light  and  shade  upon  that  side  of  the  ring  next  to 
the  ichnography,  draw  lines  through  the  points  a,p,g, 
parallel  to  the  sides  A,  E,  I,  as  are  shown  by  the 
dotted  lines,  which  will  give  lines  of  shade  on  the 
imder  side  of  each  cylindrical  part.  The  lines  for 
one  quarter  of  the  ring  being  found,  the  other  quar- 
ter, on  the  other  side  of  the  seat  A  C,  may  be  found 
from  the  last  quarter,  each  being  in  the  same  order, 
receding  from  the  line  A  C,  or  drawing  towards  it. 
One  half  being  now  found,  the  other  half  will  be 
found  by  observing  that  opposite  sides  of  the  ring 
are  parallel  to  each  other ;  and,  consequently,  if  one  is 
found,  the  other  will  also  be  found ;  for  the  light  will 
be  at  the  same  distance  upon  the  same  sides  of  that 
which  is  to  be  found  as  that  cylinder  which  is  found. 
Then  to  find  the  lightest  lines  on  the  elevation,  Fig.  2, 
and  also  those  lines  which  will  be  the  boundaries  of 
the  light  and  shade,  proceed  as  follows :  — 

Through  the  points  n,  o,  p,  q,  draw  the  lines  n  N, 
o  O,  /?  P,  (7  Q,  perpendicular  to  the  elevation,  cutting 
the   line   P   K,   which  represents   a  plane   passing 


70 


SHADOWS. 


through  the  axes  of  all  the  straight  cylinders  at  the 
points  P,  Q,  N,  O ;  make  P  H  equal  top  k;  from  Q, 
make  Q,  E  equal  to  q  e ;  from  N,  make  N  D  equal  to 
II  d;  from  O,  make  O  A  equal  to  o  a;  then  through 
(he  points  II,  D,  E,  A,  Fig.  2,  draw  lines  parallel  to 
P  K;  tlien  will  the  lines  H  and  D  represent  the  lines 
of  light,  and  E  and  A  will  represent  the  lines  of 
shade.  Now,  since  the  side  D  A,  in  the  elevation, 
Fig.  2,  represents  the  cylindrical  part  A  B  on  the 
ichnography,  and  because  that  the  lines  of  light  and 
shade  arc  in  the  same  order  on  each  side  of  A  B, — 
that  is,  the  light  and  shade  will  be  the  same  height 
from  the  plane  of  ichnography,  on  each  of  the  cylin- 
drical parts  that  are  equidistant  from  the  cylindiical 
part  A  B,  on  each  side  of  it,  and,  consequently,  will 
be  represented  on  each  of  the  cylindrical  parts,  Fig.  2, 
equidistant  from  A  D,  at  the  same  altitude,  —  then 
make  P  H  and  Q,  E,  the  next  cylindrical  part  to  the 
centre  of  the  elevation,  equal  to  P  H  and  Q,  E,  on 
the  outside  cylinth-ical  part,  which  the  side  E  F,  on 
the  ichnography,  represents  ;  make  S  M  and  R  G,  in 
the  elevation,  equal  to  s  m  and  r  g-  on  the  ichnog- 
raphy ;  the  height  of  the  lines  on  each  side  of  the 
elevation  representing  the  light  and  shade  being 
taken  from  its  corresponding  place  on  the  ichnog- 
raphy, as  is  already  shown,  will  complete  the  lines 
of  light  and  shade  on  the  elevation. 

OBSERVATIONS. 

1.  If  the  seat  ot  the  sun's  rays  be  drawn  on  any 
plane,  and  if  a  cylinder  lay  on  that  plane  with  its 
axis  perpendicular  to  its  seat,  and  parallel  to  the 
plane,  the  lightest  line  on  the  cylinder  will  be  nearer 
the  plane  in  this  position  than  in  any  other.  2.  But 
if  the  axis  of  the  cylinder  make  oblique  angles, 
then  the  line  of  light  will  be  higher  on  the  cylinder. 
3.  Again :  if  the  axis  of  the  cylinder  be  parallel  to 
the  seat  of  the  sun,  the  lightest  line  on  the  cylinder 
in  this  case  will  be  at  its  greatest  distance  from  tlic 
plane,  because  then  the  line  of  light  will  be  wliere  a 
plane  passing  through  the  axis  of  the  cylinder  cuts 
the  upper  surface  perpendicular  to  the  plane  on 
which  the  cylinder  lies ;  the  line  of  light  in  the  fii-st 
position  of  the  cylinder  is  brighter  than  the  line  of 
light  in  the  second  position,  and  the  line  of  light 
in  the  second  position  of  the  cylinder  is  brighter 
than  the  line  of  light  in  the  tliird  position ;  the  axis 
of  the   cylinder  in   all  these   cases   being  parallel 


and  equidistant  from  the  plane  of  the  ichnogra- 
phy ;  consequently,  the  lines  of  light  in  the  first 
and  third  positions  of  the  cylinder  arc  the  extremes 
of  all  the  varieties  which  happen  between  these  two 
positions  ;  that  is,  the  first  is  the  lightest  possible,  and 
the  tliird  is  the  darkest  possible.  The  boundaries  of 
light  and  shade,  called  in  this  book  the  lines  of  shade, 
or  those  lines  which  separate  the  light  side  from  the 
dark  side,  are  always  at  a  quadrant's  distance  from 
each  other ;  and,  consequently,  that  arc  which  is  the 
under  line  of  darkness  in  the  first  position  will  be 
higher  in  the  second  position,  and  still  higher  in  the 
third ;  and  if  a  plane  be  made  to  touch  the  cylin- 
der upon  that  line,  it  will  be  perpendicular  to  the 
plane  on  which  the  cylinder  lies,  and,  therefore,  its 
ichnography  will  be  represented  by  the  edge  of  the 
cylinder.  Now,  suppose  that  cylinder  to  be  turned 
round  by  moving  continually  the  same  way,  until  the 
axis  of  the  cylinder  comes  into  that  position  in  which 
the  axis  would  be  perpendicular  with  its  seat,  then 
the  line  of  darkness  would  be  in  its  highest  position. 

Plate  19. 

PROBLEM  VI. 

To  find  tlie  lightest  line,  also  tlie  line  that 
divides  the  lightest  side  from  the  dark  side 
on  the  ichnography  and  elevation  of  a  cir- 
cular ring. 

Let  A  C  be  the  seat  of  the  sun,  or  any  line  parallel 
to  it,  passing  through  the  centre  C  of  the  ichnogra- 
phy, (Fig.  1,)  cutting  the  thickness  of  the  ring  at 
B  and  H,  and  let  B  C  D  be  the  sun's  altitude ;  take 
the  point  G,  at  one  quarter  of  the  circumference  of 
the  ring,  distant  from  the  point  B ;  and  take  any 
points  E  and  F  in  the  circumference  bet^^een  B  and 
G,  and  draw  the  lines  E  C,  F  C,  and  G  C,  cutting 
the  inside  of  the  ring  at  I,  K,  and  L;  through  the 
point  B  draw  the  lines  B  M,  B  N,  and  B  U,  each  re- 
spectively perpendicular  to  E  C,  F  C,  and  G  C,  cut- 
ting E  C,  F  C,  and  G  C,  at  O  and  P ;  make  O  M, 
P  N,  and  C  U,  on  B  II,  E  I,  F  K,  and  G  L,  as  diam- 
eters; describe  circles  whose  centres  are  a,  b,c,a; 
through  these  centres  draw  the  lines  c,  d,  c,  m,  c,  n, 
and  ?«',  i(,  parallel  to  C  D,  C  M,  C  N,  and  C  U,  cut- 
ting the  circles  at  a,  m,  n,  n,  and  c,  c,  c,  w ;  also, 
through  the  centres  a,  b,  c,  v,  draw  lines  i,  q,  p,  s,  k,  y, 
and  L  G,  respectively  perpendicular  to  C  D,  C  M, 


ri.jii 


,7 


SHADOWS. 


71 


C  N,  and   C  U,  cutting  tlie  circle  at  i,  q,  p,  s,  k,  y, 
L  and  C>. 

Through  the  points  (/,  w,  n,  u,  draw  the  lines  d,  g, 
m,  e,  n,  o,  and  v,  v,  perpendicular  to  the  diameters 
B  H,  E  I,  F  K,  and  G  L,  cutting  B  H,  E  T,  F  K,  and 
G  L,  respectively  at  the  points  g;  c,  o,  v  ;  draw  a  curve 
which  will  be  part  of  the  line  of  light  for  one  quarter ; 
also  through  the  points  </,  s,  y,  draw  the  lines  q,  r,  s,  t, 
and  y  x,  cutting  the  diameters  at  r,  f,  x;  then  through 
the  points  r,  t,  x,  and  L,  draw  a  curve  line  r  t  xIj, 
which  will  be  the  upper  line  of  shade  for  that  quar- 
ter, or  that  line  which  divides  the  dark  side  from  the 
light  side,  upon  the  upper  side  of  the  ring  on  that 
half  which  is  next  to  the  luminary. 

One  quarter  being  now  found  of  the  line  of  light 
and  shade  on  the  ichnography  of  the  visible  side  of 
the  ring,  the  other  three  quarters  will  be  found  from 
that  quarter  which  is  already  found,  in  the  same 
manner  as  in  the  last  problem,  and  the  points  D,  M, 
N,  U,  I,  P,  K,  G,  also  in  the  elevation  of  the  curves 
D,  I\I,  N,  U,  and  I,  P,  K,  G,  being  drawn,  then 
D  ai  N  U  will  be  the  line  of  light,  and  I  P  K  G  the 
line  of  shade. 

Plate  20. 

PROBLEM   VII. 

To  represent  the  lines  of  equal  gradation  on 
the  surface  of  a  sphere  given  ;  the  seat  of  a 
ray  of  light  on  the  plane  of  projection,  and 
the  elevation  of  the  ray. 

Let  A  B  be  the  diameter  of  the  sphere  and  seat  of 
the  sun.  Find  the  centre  C,  and  describe  a  circle 
with  the  radius  C  A  or  C  B  ;  this  cii'cle  will  represent 
the  contour  of  the  sphere.  Make  the  angle  A  C  D 
equal  to  the  elevation  of  the  ray  above  the  seat  C  A; 
and  let  C  D  be  produced  so  as  to  cut  the  circumfer- 
ence line  in  D  and  E.  Draw  the  lines  F  G,  H  I, 
K  A,  L  jM,  N  O,  P  Q,  perpendicular  to  D  E,  to  cut 
the  cu-cle  at  the  points  F,  G,  H,  I,  K,  A,  L,  M,  N,  O, 
P,  Q ;  then  will  F  G,  H  I,  K  A,  L  RI,  N  O,  P  Q,  be 
the  diameters  of  circles  which  have  equal  intensities 
of  light  around  each  circumference  on  the  sphere. 
Draw  D  R,  G  S,  F  T,  H  V,  K  C,  L  W,  NX,  P  Y 
perpendicular  to  B  A;  then  E- will  be  the  projected 
point,  representing  the  lightest  point  on  the  surface  ; 
T  S  is  the  shorter  axis  of  the  ellipsis,  and  F  G  the 
greater.  Describe  the  ellipsis  aT  b  s,  which  will  rep- 
resent a  circle  of  equal  intensity  of  light  in  every  part 


of  its  circumference  on  the  surface  of  the  sphere.  In 
like  manner,  if  the  ellipsis  c  Y  d  e  he  drawn,  it  will 
represent  another  circle  of  equal  intensity.  Proceed 
in  this  manner,  and  represent  all  the  intermediate  cir- 
cles of  the  sphere  to  that,  the  diameter  of  which  is 
P  Q,  where  a  ray  of  the  sun  would  at  any  point  be 
a  tangent,  and  the  representation  of  this  last  circle, 
K  Y  Z,  will  be  the  line  of  separation  of  light  and 
shade ;  then  every  succeeding  ellipsis  towards  the 
lightest  point  R  wiU  represent  graduating  lines  con- 
tinually lighter. 

PROBLEM  VIII. 

Given  the  ichnography  and  elevation  of  a  cyl- 
inder, havuig  a  square  projecture  or  abacus, 
and  the  seat  of  the  sun  on  the  ichnography, 
also  its   seat  on  the  elevation ;    to  find  the 
shadow  of  the  abacus,  also  the  line  of  light 
and  shade  on  the  cylinder. 
Let  A  H  I  K  L  ]\I  N  O  B  be  the  ichnography  of 
the  cylinder ;  D  E  F  G  that  of  the  abacus  ;  V  W  the 
elevation  of  the  cylinder ;  and  E  F  the  elevation  of 
the  abacus  ;  let  C  F  be  the  seat  of  one  of  the  sun's 
rays  on  the  ichnogi-aphy,  passing  through  the  centime 
C ;  draw  F  o,  maldng  an  angle  with  E  F,  equal  to 
the  angle  which  the  seat  of  any  of  the  rays  make 
with  E  F ;  through  C  draw  C  H  perpendicular  to 
C  O,  cutting  the  ichnogi'aphy  at  H ;  between  the  points 
H  and  O,  take  any  points  I,  K,  L,  M,  and  N;  then 
through  the  points  H,  I,  K,  L,  M,  N,  draw  lines  B  B, 
I  Q,  K  R,  L  S,  M  T,  N  U,  paraUel  to  C  F,  cutting 
H  P  at  P,  Q,  R,  S,  T,  U ;  through  the  points  P,  Q, 
R,  S,  T,  U,  di-aw  lines  parallel  to  F  o ;  also  through 
the  points  B,  I,  K,  L,  JM,  N,  O,  draw  lines  H  /*,  I  i, 
K  k;  L  /,  M  m,  N  w,  O  o,  paraUel  to  the  sides  of  the 
cylinder,  cutting  P  /;,  Q  i,  R  k,  S  /,  T  m,  U  n,  F  o,  at 
the  points  /;,  i,  k,  I,  m,  n,  o  ;  through  these  points  draw 
a  curve,  and  it  will  be  the  shadow  of  the  abacus ;  H  h 
will  be  the  line  of  shade,  and  O  o  the  line  of  light. 

PROBLEM  IX. 

Given  the  ichnography  and  elevation  of  a  cylin- 
der having  a  circular  projection  over  it ;  the 
seat  of  the  sun  on  the  ichnography;  also  its 
seat  on  the  elevation  being  given  ;  to  find  the 
shadow  of  the  projecture  on  the  cylinder; 
also  the  line  of  light  and  shade. 
Fig.  2.  Let  A  D  E  F  G  H  I  B  be  the  ichnography 


72 


SHADOWS. 


of  the  cylinder,  R  K  L  M  N  O  P  Q  the  ichnography 
of  the  projection ;  let  U  T  be  the  elevation  of  the 
cylinder,  and  V  S  that  of  the  projecture;  also,  let 
C  O  be  the  seat  of  the  sun's  rays,  passing  through 
the  centre  C  of  the  ichnography,  and  o  h  the  scat  of 
the  sun  on  the  elevation. 

Through  C  draw  C  D  perpendicular,  cutting  the 
circvimference  of  tiie  inner  circle  at  D;  take  any  point 
E,  F,  G,  I,  B,  in  the  circumference ;  ch-aw  the  lines 
B  K,  E  L,  F  M,  G  N,  H  O,  I  P,  and  B  O,  parallel 
to  C  IT,  cutting  the  outward  circle  at  the  points  K,  L, 
M,  N,  O,  P,  Q ;  from  the  points  D,  E,  F,  G,  H,  I,  draw 
the  Imes  D  rf,  E  e,  F/,  Gg-,  H  h,  I  i;  also,  through 
the  points  K,  L,  M,  N,  O,  P,  Q,  draw  the  lines  K  k, 
L  /,  M  m,  N  n,  O  o,  V  p,  Q  q,  cutting  V  S  at  the 
points  /••,  /,  m,  n,  o,  p,  q ;  through  the  points  k,  I,  m,  n, 
o,  p,  q,  draw  k  d,  I  e,  m  f,  n  g,  o  h,  p  i,  parallel  to  o  h, 
cutting  the  lines  D  d,  E  c,  F/,  Gg-,  H  h,  I  i,  at  the 
points  d,  e,f,  g,h,i;  a  ciurve  being  traced  through 
these  points  will  be  the  representation  of  the  shadow 
upon  the  cylinder ;  D  d  will  be  the  line  of  shade, 
and  H  the  line  of  light. 

Plate  21. 

PROBLEM  X. 

The  ichnography  and  elevation  of  the  prism 
standing  upon  a  polygonal  base,  having  the 
projecture  or  cap  of  the  same  figure  upon  it, 
projecting  equally  over  its  sides ;  given  the 
seat  of  the  sun's  rays  on  the  plane  of  the 
ichnography,  and  also  on  the  elevation ;  to 
project  the  shadow  of  the  cap  on  the  prism, 
and  also  on  a  plain  parallel  to  the  axis  of 
the  prism. 

Let  A  B  C  D  E  F  G  be  the  ichnogi-aphy  of  the 
prism,  H  IJ  K  L  M  N  the  ichnogi-aphy  of  the  cap 
W  A  and  G  P,  parts  of  the  ichnography  of  the  plane 
on  each  side  of  the  prism,  J  W  be  the  projection  of  a 
ray  on  the  ichnography,  and  j  lu  on  the  elevation. 
From  all  the  points  H,  I,  J,  K,  L,  M,  N,  in  the  ich- 
nography of  the  angles  of  the  cap,  draw  the  lines 
H  /(,  I  i,  J  j,  K  k,  L  I,  M  «!,  N  n,  perpendicular  to 
W  P,  to  cut  the  under  side  of  the  cap  at  h,  i,j,  k,  I, 
m,  n.  Draw  the  lines  A4  «,  B  5  i»,  C  6  c,  D  7  </,  E  8  e, 
F  9/,  G  10  g-,  perpendicular  to  W  P,  cutting  the  bot- 
tom of  the  prism  at  4,  5,  6,  7,  8,  9,  10,  then  the  lines 
4  o,  5  6,  6  c,  7  rf,  8  e,  9/,  10  g,  represent  the  angles 


on  the  elevation.  Draw  the  lines  H  Z,  I  X,  J  'W, 
K  Q,  L  R,  M  T,  N  U,  parallel  to  J  W,  cutting  the 
ichnography  of  the  plane  at  the  points  Z  X  W,  and 
the  ichnography  of  the  prism  at  Q,  R,  T,  U.  Through 
the  points  h,  i,j,  k,  I,  in,  n,  the  projection  of  the  an- 
gles of  the  cap  on  its  mider  edges,  and  parallel  to 
j  «',  draw  the  projections  of  the  rays  h  z,  i  x,j  u;  k  q, 
I  r,  m  t,  n  v.  Draw  the  perpendiculars  Z  z,  X.r,  W  iv, 
Q  (7,  R  r,  T  <,  U  u,  then  the  points  z,  x,  to,  are  the 
projections  of  the  angles  of  the  cap  on  the  plane,  and 
q,  r,  t,  t(,  the  projection  of  the  other  angles  on  the 
elevation  of  the  prism.  Draw  C  Y,  to  touch  the 
prism  at  C,  and  draw  Y  j/  perpendicular  to  W  P, 
then  Y  y  will  be  the  termination  of  the  shadow  of 
tlie  body  of  the  prism  on  the  wall.  Then,  because 
that  the  point  q  is  in  the  plane  G  c  d7,  the  point  r  in 
the  plane  7  (Z  e  8,  and  the  points  t  and  v,  in  the  plane 
9/g-  10,  and  the  lines  j,  k,  I,  m,  n,  parallel  to  these 
planes,  the  lines  /,  k,  1,  m,  n,  will  make  parallel  shad- 
ows ;  therefore,  draw  q  c,  r  d,  t  v,  parallel  toy,  k,  I,  ot 
■m  n,  to  cut  c  6  in  c,  k  7  in  d,  and  G  g-  at  n ;  join  d  q; 
then,  to  find  the  depth  of  the  shadow  of  I  m  on  the 
elevation,  draw  Sf  s  on  the  ichnogi-aphy  parallel  to 
J  W ;  draw  Sf  &  perpendicular  to  W  P,  likewise  Sf  s, 
parallel  to  the  ray  on  the  elevation,  and  S  s  parallel 
to  the  axis  of  the  prism  ;  then  s  is  the  depth  of  the 
shadow;  but  as  the  projections  of  the  exh-emities  of 
I VI  fall  upon  the  adjacent  planes  at  ?•  and  t,  draw 
e  f  through  s,  cutting  8  e  at  e,  and  9/ at  f ;  then  join 
e  r,  f  t.  Lastly :  draw  G  V  on  the  ichnogi-aphy  par- 
allel to  W  J,  cutting  the  projection  of  the  cap  at  V; 
draw  V  v  perpendicular,  cutting  the  cap  at  v,  and 
draw  V  g  parallel  to  the  rays  on  the  elevation,  and 
join  u  g;  then  c  q  d,  r  e  {  t  tt  g  will  be  the  shadow 
of  the  cap  on  the  elevation ;  but  as  the  shadow  of  the 
parts  of  the  abacus  H  I,  I  J,  will  be  from  the  top  of 
tiie  cap,  make  lu  1,  x  2,z  3,  parallel  to  the  angles  of 
the  prism  on  the  elevation,  and  equal  to  the  thick- 
ness of  the  cap.  Join  1,  2 ;  2;  2,  3  ;  then  will  3,  2, 
1  10  7/  be  the  shadow  of  the  abacus  on  the  wall. 
Tlirough  g  di-aw  g  m  and  k  i  in  the  same  straight 
line  with  g  m,  cutting  3  2  at  k  ;  then  i  k  2,  /  w  y,  is 
the  complete  shadow  of  the  cap  on  the  plane. 

Much  after  the  same  manner  rnay  the  shadow  of 
a  cylinder  be  found,  having  a  circular  projection  over 
it,  as  is  shown  at  Fig.  2,  and  also  the  shadow  of  the 
cylinder  projecture  may  be  found  on  a  plane  parallel 
to  the  axis  of  the  cylinder,  having  the  same  tiling 
given  as  before ;  but  for  more  easy  inspection,  letters 


I'l.J) 


4L^/ 


3  /A 


T 


\  ■.">'. 


L* 


\¥ 

i 

''  :   i  i 

... 

■' 

'/ 

\n\  ..- 

,<•' 

' 

Fi)>.  1 . 

% 

1 

N''\l. 

y 

::■-». 

i 

''              1 

\K.V;  -> 

N> 

■    :     \ 

] 

V: 

:     :■■  \ 

II 

3Jv' 

:  '•   I'.'T 


Si^.  i     /&. 


/ 


I'l 


SMAiD.SWS 


D^z 


lllllllllllllllllllIlllllllllllllllllllllllllllllllllllllllllllllllllJllllllllllllllll^lP^ 


SHADOWS. 


78 


are  placed  on  the  ichnography  and  elevation,  repre- 
senting the  correspondiiig  parts  of  each  other ;  that 
is,  capital  letters  are  placed  on  the  ichnography,  and 
small  letters  of  the  same  name  on  the  elevation, 
representing  those  of  the  same  name  on  the  ichnog- 
raphy. 

PROBLEM  XI. 

Given  the  seat  and  altitude  of  the  sun  on  any 
plane,  also  the  seat  and  altitude  of  a  Ime  to 
the  same  plane ;  to  determine  the  shadow  of 
the  line  upon  that  plane. 

Let  K  L  be  the  seat  of  the  line  upon  the  plane, 
and  G  H,  Fig.  3,  the  angle  wliich  the  line  makes 
with  its  seat ;  make  the  angle  M  K  L,  Fig.  2,  equal 
to  the  angle  H  G  I ;  through  L  draw  L  M,  perpen- 
dicular to  K  L,  cutting  K  M  at  M ;  also,  through  L 
draw  L  O  parallel  to  the  seat  of  the  sun.  Again : 
through  L  draw  L  N  perpendicular  to  L  O,  and 
make  L  N  equal  to  L  M ;  then  upon  the  right  line 
L  N,  and  from  the  point  N,  make  the  angle  L  N  O 
equal  to  the  complement  of  the  angle  of  the  sun's 
inclination  to  a  right  angle ;  produce  N  O,  cutting 
L  O  at  O;  then  join  the  points  K  and  O,  and  the 
line  K  O  will  be  the  shadow  required. 

Tliis  problem  will  be  found  of  great  use  in  finding 
the  shadows  upon  inclined  planes. 

XoTE.  If  the  seat  and  altitude  of  the  8>in  be  given  on  any  other 
plane,  making  a  given  angle  ■with  the  plane  on  which  the  shadow 
is  to  be  projected,  the  sun's  altitude  and  seat  may  be  found  by 
Problem  II. 

PROBLEM  XII. 

Given  the  seat  and  angle  of  inclination  of  the 
sun  on  the  horizon,  and  the  intersection  of 
a  plane  perpendicular  to  the  horizon ;  to  de- 
termine the  angles  which  a  plane  of  shade, 
made  by  a  right  line,  parallel  both  to  the 
horizontal  and  perpendicular  planes,  will 
make  with  each  of  the  planes. 

Let  A  B  be  the  seat  of  the  sun  on  the  horizon,  and 
A  A  D,  as  Fig.  1,  the  angle  of  inclination  to  the  seat 
A  B,  and  let  C  B  be  the  intersection  of  a  plane  per- 
pendicular to  the  horizon ;  take  any  point  C  in  C  B, 
and  from  C  draw  C  A  perpendicular  to  C  B,  cutting 
A  B  at  A ;  from  A,  draw  A  E  perpendicular  to  A  C, 

10 


and  A  D  perpendicular  to  A  B,  cutting  D  B  at  D ; 
make  A  E  equal  to  A  D,  and  join  C  E ;  then  will 
the  angle  B  C  E  be  the  angle  which  the  plane  of 
shade  makes  with  the  perpendicular  plane,  and  the 
angle  ACE  the  angle  which  the  plane  of  shade 
makes  with  the   horizon. 

This  problem  will  be  very  useful  in  shading  mould- 
iiigs  which  project  from  planes  that  stand  perpendic- 
ular to  the  horizon,  the  sun's  altitude  and  seat  beinc 
given  to  the  horizon,  as  will  be  shown  in  the  next 
problem. 

Plate  32. 

PROBLEM  XIII. 

A  moulding  of  any  kind  being  given,  and  the 
angle  which  a  plane  of  shade  makes  with  a 
perpendicular  part  of  the  moulding,  either 
being  given  or  found  by  the  last  problem, 
ha^ing  the  sun's  altitude  and  seat  on  the 
horizon;  to  deteimine  the  shadow  on  the 
moulding. 

Let  the  ovolo,  fillets,  and  hollow.  Fig.  1,  be  the 
given  moulding ;  draw  C  D  parallel  to  the  inclination 
which  the  plane  of  shade  makes  with  the  vertical 
part  of  the  moulding,  touching  the  ovolo  at  C,  and 
cutting  the  vertical  part  below  D ;  then  a  line  drawn 
through  D  perpendicular  to  the  fillet  will  give  the 
lower  edge  of  the  shadow,  and  an  imaginary  line, 
supposed  to  be  drawn  through  C,  will  give  the  line  of 
shade ;  and  if  a  line  is  drawn  through  A,  the  lower 
edge  of  the  fillet  above  the  ovolo  parallel  to  C  D, 
cutting  the  ovolo  at  G,  then  a  line  being  drawn 
through  B,  parallel  to  the  fillet,  will  give  the  edge  of 
the  shadow  from  the  fillet. 

Much  in  the  same  manner,  may  the  shadow  upon 
the  cima  reversa  and  cima  recta  be  found,  as  shown 
by  the  dotted  lines. 


ON     MOULDINGS 

Plate  22. 

The  form  or  shape  of  mouldings,  in  most  cases, 
may  be  ascertained  from  the  various  degrees 
of  light  and  shade  upon  them,  without  ob- 


74 


SHADOWS. 


serving  the  profiles;    which  will  appear  evi- 
dent from  the  following  observations:  — 

Observations  on  Surfaces,  and  their  Poiver  to  reflect 
Light. 

It  has  already  been  observed  in  the  second  propo- 
sition, that  if  the  sun's  rays  fall  upon  a  reflecting 
plane,  the  angles  made  by  the  reflected  rays,  with 
perpendiculars  at  the  impinging  points,  will  be  equal 
to  the  angles  made  by  their  corresponding  incident 
rays  with  the  said  perpendiculars ;  so  that  the  rays 
in  this  case  will  have  only  one  direction  after  reflec- 
tion :  but  by  experiment  wc  are  shown  that  there  is 
no  such  thing  as  a  perfect  plane ;  for,  if  a  sm-face  is 
even  polished  to  the  greatest  degree,  yet  this  polished 
surface  will  be  but  rough  and  uneven  ;  for,  if  viewed 
through  a  microscope  having  a  great  magnifying 
power,  the  surface  will  appear  quite  irregular,  and 
the  different  parts  of  the  surface  will  be  inclined  to 
any  fixed  plane,  in  all  manner  of  directions;  and, 
consequently,  if  the  sun's  rays  fall  upon  such  a  sur- 
face, the  rays  will  not  be  enthrely  reflected  in  the  same 
direction,  but  a  great  part  of  them  will  be  reflected 
in  all  manner  of  directions  by  the  different  positions 
of  the  surface,  by  Proposition  IV.  It  may  be  ob- 
served, that  the  higher  any  surface  can  be  polished, 
the  nearer  it  approximates  to  a  plain,  and,  conse- 
quently, the  rays  wUl  be  more  and  more  reflected  in 
the  same  direction ;  but  there  is  no  surface  which 
will  reflect  the  sun's  rays  entirely  in  the  same  direc- 
tion ;  that  is,  parallel  to  each  other ;  but  a  great  part 
of  them  will  be  reflected  in  all  manner  of  directions : 
it  will  be  also  necessary  to  observe,  that  the  power 
of  reflection  will  depend  very  much  on  the  lightness 
of  the  color  of  materials ;  for  the  darker  any  sub- 
stance iS;  the  more  will  the  rays  of  light  be  absorbed 
in  that  substance,  and,  consequently,  will  have  a  less 
power  to  reflect. 

White,  being  the  lightest  of  all  colors,  will  reflect 
the  most  rays ;  and  the  more  any  substance  inclines 
to  a  white,  the  greater  power  wiU  that  surface  have 
to  reflect  the  rays  of  light. 

CASE  I. 

Observations  on  Mouldings  in  Shade. 

If  the  sun's  rays  fall  upon  any  building,  also  upon 

the   ground  or  horizon   below  the  building,  and  if 

there  are  any  projectures  from  the  building,  such  as 

mouldings  or  other  ornaments,  and  if  any  of  the 


parts  of  those  mouldings  or  ornaments  are  entirely 
in  shadow  by  the  projecture  of  somethmg  else  which 
prevents  the  rays  of  the  sun  from  falling  upon  them, 
those  parts  of  the  mouldings  which  are  in  shade  will 
become  visible;  for,  besides  a  reflection  from  the 
ground,  there  will  be  a  strong  reflection  from  the 
surface  of  the  Iniilding,  immediately  under  the 
mouldings  or  ornaments.  It  has  already  been  ob- 
served, that  these  rays  will  be  reflected  in  all  direc- 
tions, and,  consequently,  a  part  of  them  wiU  be  re- 
flected upwards  on  the  mouldings  above,  and,  there- 
fore, will  show  hght  and  shade  on  the  mouldings 
according  as  the  reflected  rays  fall,  more  or  less,  per- 
pendicular on  their  surfaces. 

Hence  the  reason  why  all  perpendicular  sides  of 
fillets  will  be  darker  in  shade  than  the  horizon- 
tal  sides. 

An  ovolo,  having  a  projecture  over  it,  so  as  to  pre- 
vent the  sun's  rays  from  falling  upon  it,  the  reflected 
rays  being  more  and  more  mclined  from  the  under 
edge  towards  the  upper  edge,  wiU  be  lightest  below, 
and  will  be  gradually  darker  and  darker  upwards. 

A  cavctto  or  hollow,  immersed  m  shade,  will,  for 
the  same  reason,  be  darkest  below,  and  will  be  con- 
tinually lighter  to  the  upper  edge. 

A  cima  reversa,  in  shade,  will  be  darkest  above  and 
below,  and  lightest  in  the  middle ;  for  this  moulding 
is  composed  of  an  ovolo  above  and  a  cavetto  below. 

A  cima  recta,  in  shade,  will  be  hghtest  above  and 
below,  and  darkest  in  the  middle. 

These  are  general  rules  for  shading  horizontal 
mouldings. 

CASE  II. 
Observations  on  vertical  Mouldings. 

All  upright  perpendicular  mouldings,  in  shade,  or 
being  in  part  so,  will  receive  a  reflection  from  those 
smrfaces  which  are  next  to  them ;  for  they  cannot 
receive  a  reflection  from  the  contrary  side,  by  reason 
of  their  projection,  which  wiU  prevent  the  ray,  re- 
flected from  that  side,  from  falling  on  them. 

Therefore,  it  is  plain,  in  these  cases,  the  forms  of 
mouldings  may  be  known  by  reflection. 

Artists  give  this  rule  for  shadowing:  that  is,  to 
shade  all  mouldings  or  other  ornaments  which  are  in 
shade,  inverse  to  those  on  which  the  sun's  rays  fall, 
from  the  contrary  side  of  the  reflected  rays.  But  this 
rule  is  not  only  very  uncertain,  depending  much  on 
the  situation  of  other  objects  which  surround  thcs* 


SHADOWS. 


75 


mouldings  or  ornaments,  but  in  some  cases  very  erro- 
neous, as  in  the  example  of  mouldings  perpendicular 
to  the  horizon  ;  for  mouldings  in  this  situation,  as  has 
been  observed,  will  receive  a  reflection  from  that  side 
which  is  next  to  the  front  of  the  moulding,  if  some- 
thing else  docs  not  project  to  a  great  distance  from 
that  surface  from  wliich  the  reflection  comes.  K  a 
cylinder  or  column  is  attached  to  a  wall  in  a  vertical 
position,  and  if  it  has  any  projecture  over  it,  so  as  to 
cause  that  part  under  the  projecture  to  be  in  shade 
quite  round  the  cylinder,  there  will  not  only  be  a  re- 
flection from  the  wall  on  the  contrary  side  of  the 
cylinder,  to  the  sun  upon  that  side  of  the  cylinder 
which  is  next  to  it,  but  also  from  that  part  of  the  wall 
on  that  side  of  the  cylinder  next  to  the  sun,  which 
will  make  that  part  of  the  cylinder  which  is  in  shadow 
lightest  at  the  two  sides  and  darkest  in  the  middle. 
Something  of  the  same  kind  may  be  seen  in  Ionic 
columns  attached  to  a  wall,  where  it  may  be  observed 
when  the  sun  shines  upon  one  side  of  them  ;  suppose 
that  side  of  the  column  which  is  on  the  right  hand, 
then  the  right  hand  volute  will  throw  a  shadow  upon 
the  light  side  of  the  column,  which  shade  Avill  be 
lightest  on  that  edge  which  is  next  to  the  wall  and 
to  the  luminary,  and  darkest  at  that  edge  next  to  the 
middle  of  the  column. 

CASE  III. 

Observations  on  Mouldings  in  Shade,  when  situate  on 
the  Side  of  an  Object  ivhich  is  entirely  in  Shade^ 
and  also  the  Ground  under  that  Side  in  Shade. 

In  one  building  where  one  end  or  side  is  entirely 
in  shade,  and  also  a  great  part  of  the  ground  under 
that  end  in  shade,  there  wUl  be  little  or  no  reflection 
from  the  ground  upwards,  nor  from  the  surface  of 
the  building,  and,  consequently,  little  reflection  upon 
the  mouldings  from  below ;  the  only  light  which  they 
receive  is  from  a  kind  of  scattered  or  confused  rays 
in  the  atmosphere,  and  small  reflections  from  the 
horizon  ;  and,  therefore,  horizontal  mouldings,  or  or- 
naments, in  this  situation,  which  have  but  small  pro- 
jectures  over  them,  will  have  a  contrary  effect  to 
mouldings  in  shadow  situate  on  the  light  side  of  an 
object. 

An  ovolo,  placed  horizontally,  and  whose  greatest 
projecture  is  upwards,  upon  the  dark  side  of  an  ob- 
ject, will  be  lightest  above,  and  continually  darker  and 
darker  to  the  under  edge. 


A  cavello,  having  its  greatest  projecture  upwards, 
placed  horizontally  on  the  dark  side  of  an  object,  will 
be  darkest  above,  and  continually  lighter  and  lighter 
to  the  under  edge. 

Kcima  reversa,  placed  horizontally  on  tlie  dark  side 
of  the  object,  having  its  greatest  projection  upwards, 
will  be  darkest  in  the  middle,  and  lightest  above  ajid 
below. 

A  cima  recta,  whose  greatest  projecture  is  upwards, 
and  placed  horizontally,  will  be  darkest  above  and 
below,  and  lightest  in  the  middle. 

All  horizontal  projectures  on  the  dark  side  of  an 
object  will  condense  the  shade  under  them,  and,  con- 
sequently, will  appear  more  or  less  dark  according 
as  the  projecture  is  more  or  less. 

These  are  general  rules  for  shading  mouldings  on 
the  dark  side  of  an  object  from  scattered  light ;  how- 
ever, there  are  some  exceptions  to  these  rules  —  that 
is,  when  any  of  these  mouldings  have  a  very  great 
projecture  over  them,  this  projecture  will  hinder  the 
scattered  rays  from  falling  upon  the  mouldings ;  but 
as  they  will  receive  a  small  reflection  from  the  hori- 
zon below,  the  most  of  the  scattered  and  reflected 
rays  will  fall  obliquely  on  the  moulding;  thus  the 
lighted  place  of  an  ovolo  will  not  be  exactly  on 
the  under  edge,  but  somewhere  between  the  under 
and  upper  edge,  and  will  be  nearest  to  either,  ac- 
cording as  the  shadow  on  the  ground  is  less  or 
more  distant  from  that  side  of  the  object,  and  ac- 
cording as  the  projecture  over  the  moulding  is 
more  or  less,  and  also  according  to  the  position 
and  distance  of  other  surrounding  objects ;  all  these 
different  circumstances  combining  together  wUl  vary 
the  places  of  light  and  shade  on  horizontal  mould- 
ings, which  are  situate  on  the  dark  side  of  an 
object. 

An  horizontal  cavetto  on  the  dark  side  of  an  object 
having  a  projecture  over  it  as  before,  the  lightest 
place  will  be  somewhere  between  the  upper  and 
under  edge,  as  in  the  ovolo,  and  both  mouldings 
would  have  actually  the  same  appearance  if  their 
profiles  could  not  be  observed,  when  most  of  the 
scattered  and  reflected  rays  are  in  a  plane,  making 
equal  angles  with  the  horizon,  and  with  that  side 
of  the  object  in  shade  —  that  is,  forty-five  degrees 
with  each  other ;  and,  consequently,  mouldings  in 
this  situation  will  be  less  distinct  than  mouldings 
in  shade  on  that  side  of  the  object  which  the  sun 
shines  on. 


76 


SHADOWS, 


Further  Observations  on  the  Effect  that  reflected  Light 
tcill  have  on  Cornices  which  have  ModiUions  or 
Mutules,  Dentils,  Sfc,  or  any  other  projecting  Or- 
naments of  a  Nature  similar  to  them. 

The  reflected  light  from  the  ground  and  from  the 
object  being  scattered  in  all  directions,  it  will  there- 
fore follow,  if  there  are  any  projecting  parts  from 
mouldings  or  cornices,  which  are  in  shadows,  such 
as  mutules,  modillions,  dentils,  &c.,  these  projecting 
parts  will  hinder  a  great  part  of  the  scattered  rays 
from  falling  in  the  spaces  between  them ;  and  there- 
fore the  spaces  will  be  deprived  of  reflection,  and, 
consequently,  will  be  much  darker  than  the  promi- 
nent parts,  even  if  these  prominent  parts  were  also 
in  shadow. 

For  this  reason,  the  intervals  between  mutules,  mo- 
dillions, dentils,  &c.,  are  darker  than  on  their  fronts, 
for  every  projecture  will  condense  the  shadow  on 
each  side  of  it,  if  recessed  on  both  sides  ;  therefore, 
the  spaces  will  be  lightest  in  the  middle,  and  darkest 
nearest  to  the  edges  of  the  mutules,  modillions,  den- 
tils, &c. ;  but  to  show  on  which  side  of  the  mutules, 
&c.,  the  greatest  shade  would  fall,  according  to  the 
place  of  the  luminary,  would  be  almost  impossible, 
as  it  depends  so  much  on  the  situation  of  other  ob- 
jects. But  suppose  all  the  surrounding  objects  in  the 
vicinity  to  be  removed,  and  the  ground  and  building 
to  be  of  a  light  color,  and  suppose  the  rays  to  pro- 
ceed from  the  right  to  the  left  hand  of  the  object,  and 
parallel  to  a  vertical  plane  which  is  inclined  at  an 
angle  of  forty-five  degrees  with  the  elevation  of  the 
object ;  then  it  is  plain  that,  since  the  angle  of  reflec- 
tion is  equal  to  the  angle  of  incidence,  the  greatest 
part  of  the  rays  which  fall  upon  the  horizon  will  be 
reflected  from  the  ground  parallel  to  the  vertical 
plane  ;  and  seeing  that  the  vertical  plane  would  be 
on  the  right  hand  of  another  vertical  plane,  perpen- 
dicular to  the  face  of  the  object  and  to  the  horizon, 
it  follows  that  most  of  the  rays  will  come  from  the 
right  hand,  and  be  reflected  towards  the  left  on  the 
object ;  and,  consequently,  any  projectures  from  cor- 
nices, as  mutules,  &c.,  which  are  in  shadow,  will  con- 
dense oi  darken  the  shade  upon  the  left  hand  of  the 
projecture,  and  that  vertical  side  of  the  mutules 
which  is  next  to  the  luminary  will  be  lighter  than  the 
other  vertical  side  on  the  left  of  the  mutule,  &c.  As 
to  the  direction  and  effect  which  most  of  the  re- 
flected rays  would  take  from  the  face  of  the  object, 


imagine  a  plane  parallel  to  the  sun's  rays,  and  per- 
pendicular to  the  face  of  the  building  or  object;  then 
most  of  the  rays  will  be  reflected  from  the  building 
or  object  downwards,  parallel  to  this  last-mentioned 
plane  ;  and  that  part  of  those  rays  which  are  reflected 
upwards  would  take  no  particular  direction  to  the 
right  or  to  the  left,  and,  therefore,  would  cause  no  sen- 
sible difference  upon  the  vertical  sides  of  the  mutules, 
but  would  reflect  most  light  upon  the  horizontal  or 
under  sides,  &c. 

What  has  now  been  said  of  mouldings  in  shade 
having  projectures  from  them,  or  of  the  recessed  parts 
of  any  object,  will  apply  to  ornaments  in  shade  which 
are  deeply  relieved ;  for  their  recessed  parts,  according 
to  the  foregoing  observations,  will  be  deprived  of  reflec- 
tion by  the  more  prominent  parts  of  them  ;  they  will, 
therefore,  be  darkest  in  their  receding  parts,  and  light- 
est on  the  prominent  parts. 

Observations  on  the  Shades  of  Projectures  from 
Buildings,  or  from  any  other  plain  Surface  which 
is  made  of  light  Materials. 

If  there  is  any  vertical  plane,  and  if  a  rectangular 
prism  is  attached  to  that  plane,  having  two  of  its 
sides  parallel  to  the  plane,  —  and,  consequently,  the 
other  two  sides  perpendiciilar  to  it,  —  then,  if  the  sun- 
shine on  the  plane  be  on  either  side  of  the  prism,  the 
other  opposite  side  of  the  prism  will  cause  a  shadow 
to  be  projected  from  its  edge  upon  the  plane  ;  and  if 
the  shadow  upon  the  plane  be  of  ^o  considerable 
breadth,  and  if  the  plane  be  extended  at  any  consid- 
erable distance  beyond  the  shadow,  then  the  lightest 
part  of  the  plane  on  which  the  rays  fall  will  reflect 
a  great  part  of  the  rays  towards  the  prism  ;  but  as 
these  reflected  rays  will  not  fall  upon  the  shadow,  it 
will  be  deprived  of  reflection  ;  but  as  the  side  of  the 
prism  which  projects  the  shadow  is  opposed  to  the 
reflected  rays,  that  side  of  the  prism  will  receive  a 
strong  reflection,  which  will  cause  it  to  appear  much 
lighter  than  the  shadow  it  throws  on  the  plane  ;  but 
if  the  shadow  be  projected  farther  on  the  plane,  it  will 
diminish  the  reflecting  surface  behind  the  prism,  and 
will  also  cause  the  reflecting  surface  to  be  at  a  gi'catcr 
distance  from  the  side  of  the  prism,  and,  consequent- 
ly, will  receive  less  reflection  from  the  plane  ;  and,  in 
general,  the  reflection  on  the  prism  will  be  continually 
diminished,  according  as  the  shadow  on  the  plane  is 
increased,  till  at  last  there  will  be  no  difference  be- 
tween the  shadow  on  the  plane  and  the  side  of  the 


Pl.l'.-J 


•swM)mv^ 


M  N 


O    V K. 


l".-l- 


::?y>?TSi 


SHADOWS. 


77 


prism  which  projects  that  shadow ;  and  if  the  plane 
be  entirely  deprived  of  light,  by  the  extensive  breadth 
of  the  shadow,  the  side  of  the  prism  will  in  general 
be  darker  than  the  shadow  on  the  plane :  but  this 
will  depend  very  much  on  the  situation  of  other 
objects. 

A  building  consisting  of  light-colored  materials, 
having  a  break  in  the  front  which  projects  a  shadow 
on  the  building,  at  a  small  distance  from  the  break, 
will,  for  the  reason  before  mentioned,  be  much  lighter 
on  the  side  of  the  break  than  the  shadow  projected 
by  it  on  the  building  behind  it ;  also,  columns  which 
are  attached  to  a  wall  will  project  a  darker  shadow 
on  the  wall  than  any  part  of  the  columns  which 
throw  the  shadow,  provided  that  the  shadow  is  not 
any  considerable  distance  from  the  column ;  for,  ac- 
cording to  the  above  observations,  the  broader  the 
shadow,  the  less  the  column  will  appear  to  be  relieved 
from  it. 

Observations  on  the  light  Side  of  the  Prism,  and  the 
Effect  that  a  Reflection  from  the  Horizon  and  from 
the  Object  will  have  on  the  Plane  behind  the  Prism. 

The  rays  of  the  sun  being  reflected  from  the  hori- 
zon in  all  directions,  the  projecture  of  the  prism  will 
prevent  a  part  of  the  reflected  rays  from  proceeding 
to  the  plane  behind  the  prism,  and,  consequently,  the 
plane  would  be  something  darker  than  the  face  of 
the  prism  which  is  parallel  to  it ;  but  the  side  of  the 
prism  adjoining  to  the  plane  will  throw  a  reflection 
upon  the  plane,  and,  therefore,  it  would  be  difficult  to 
perceive  the  difference  between  the  face  of  the  prism 
and  the  plane  parallel  behind  the  prism.  As  to  the 
difference  of  light  between  the  side  of  the  prism, 
which  is  perpendicular  to  the  plane,  and  the  plane,  it 
will  very  much  depend  on  the  situation  of  the  lumi- 
nary ;  for  if  the  luminary  is  in  a  plane  equally  in- 
clined to  both,  there  will  be  nearly  the  same  degree 
of  light  on  each ;  for  very  little  difference  will  arise 
from  the  reflection,  except  the  luminary  is  more  in- 
clined to  one  surface  than  another;  and  then  that 
surface  will  be  darker  than  the  other,  accordmg  to  the 
obliquity  of  the  rays  of  the  sun  on  that  surface. 

PROBLEM  I. 
Plate   24. 

Given  the  ichnography  and  elevation  of  a  base 
and  capital,  and   the  seat  of  the   sun's  rays 


on  the  ichnography,  and  on  the  elevation ; 
to  project  the  shadows  caused  by  the  several 
parts  of  itself,  and  the  line  of  shade  upon 
the  base. 

Imagine  the  object  to  be  sliced,  or  cut,  by  as  many 
planes,  parallel  to  the  axes  of  the  columns,*  and  to 
the  sun's  rays,  as  may  be  thought  convenient  for  the 
purpose  :  then  it  is  plain,  if  a  ray  of  light  enter  any 
of  those  planes,  that  every  part  of  the  ray  ^vill  be  in 
that  plane,  and  that  the  projecting  parts  upon  the 
edges  of  these  planes  will  withhold  the  rays  from  a 
part  of  the  edge  of  the  plane ;  and  the  lowest  point 
of  that  part  will  give  the  edge  or  projection  of  the 
shadow  of  the  part  which  throws  the  shadow :  then, 
if  a  sufficient  number  of  these  points  are  found,  a 
line  drawn  through  ihern,  with  a  steady  hand,  will 
give  the  shadow ;  the  line  of  shade  will  be  found  by 
drawing  lines  to  touch  the  several  sections  parallel  to 
the  seat  of  the  sun's  rays  on  the  elevation ;  and  a 
line  being  drawn  through  the  points  of  contact  of 
the  sections,  will  give  the  line  of  shade. 

Let  H  I  K  be  the  ichnography  of  the  abacus ; 
H  S  K  the  ichnography  of  the  ovolo ;  and  M  P  L 
that  of  the  astragal ;  the  lines  G  Y,  F  X,  E  W,  D  V, 
C  U,  B  T,  and  A  S  are  lines  drawn  parallel  to  the 
ichnography,  cutting  the  front  I  K,  of  the  abacus,  and 
from  the  seats  on  the  ichnography,  and  the  several 
seats  on  the  elevation,  the  shadows  may  be  described, 
as  is  shown  in  the  elevation :  then  lines  are  drawn  to 
touch  the  most  prominent  parts  of  those  sections ; 
and  the  places  where  they  cut  the  other  parts  of  the 
sections  will  be  the  projections  of  the  several  points 
as  before,  and  a  line  being  drawn  through  these  points 
will  give  the  shadow. 

The  part  G  F  E  is  the  shadow  from  the  abacus,  and 
D  C  B  the  shadow  from  the  ovolo ;  thus  the  point  g  in 
the  elevation  is  the  shadow  of  P ;  /  is  the  shadow  of 
N,  and  E  the  shadow  of  m ;  and  the  shadow  of  the 
other  part  of  the  abacus  would  be  where  the  dotted 
curved  line  is  represented ;  but  as  the  sun  shines  on 
the  ovolo,  in  the  middle  of  the  abacus,  it  will  throw 
the  shadow  lower  than  the  dotted  lines.  This  will 
be  found  by  drawing  lines  to  touch  the  several  sec- 
tions, which  will  give  the  points  B,  C,  D. 

*  It  is  not  absolutely  necessary  to  suppose  the  plane  parallel  to 
the  axis  of  the  column,  as  in  this  problem  ;  but  the  sections  formed 
by  planes  in  this  position  are  more  easily  found  than  in  any  other, 
for  Tvhich  reason  I  prefer  the  above  position  of  planes. 


78 


SHADOWS, 


Note.  —  That  the  line  of  shade  on  the  torus  might  have  been 
found  in  a  very  different  manner  than  is  8ho>vn  ia  this  example, 
may  be  seen  by  the  circular  ring,  plate  19. 

Much  after  the  same  manner  may  the  shadow  and 
lines  of  shade  be  found  on  the  attic  base,  as  is  shown 
in  plate  24. 

PEOBLEM  II. 
Plate  35. 

Fig.  1.  To  find  the  shadow  of  a  cylindrical 
recess  in  a  wall,  whose  axis  is  perpendicular 
to  the  plane  of  the  wall ;  having  the  seat  of  the 
sun's  rays  on  the  ichnography  and  elevation. 

Let  Fig.  1  be  the  elevation  of  the  wall,  and  C  D 
the  diameter  of  the  cyUndrical  recess ;  and  let  E  F  G  H 
be  the  ichnography ;  bisect  C  D  at  a  ;  draw  A  a  per- 
pendicular to  E  H,  cutting  it  at  A ;  through  A  draw 
A  B  parallel  to  the  seat  of  the  sun's  rays  on  the  ich- 
nography, cutting  F  G  at  B ;  through  B  draw  B  b 
parallel  to  A.  a;  and  through  a  draw  a  b  parallel  to 
the  seat  on  the  elevation,  cutting  B  Z>  at  i ;  then  on 
B  as  a  centre,  with  one  half  of  C  D,  describe  a  part 
of  a  circle,  as  is  shown  by  the  dark  line,  and  it  will 
be  the  edge  of  the  shadow. 

Much  in  the  same  manner  may  the  shadow  of  a 
recess,  which  has  a  back  parallel  to  the  plane  of  the 
wall,  be  found,  as  is  shown  at  Fig.  2. 

PROBLEM  III. 

Fig.  3.  To  find  the  shadow  of  a  recess  con- 
structed as  in  Fig.  2,  when  the  sides  of  the 
ichnography  are  inclined  to  the  intersection 
of  the  two  planes  of  the  ichnography  and 
orthography  given,  the  intci-section  of  a  num- 
ber of  planes  passing  through  the  luminary 
perpendicular  to  the  plane  of  the  elevation. 

Let  Z  6,  W  Y,  T  V,  and  Q  S  be  the  intersection 
uf  as  many  planes  passing  through  the  sun  perpen- 
dicular to  the  elevation,  and  let  Q,  R  be  the  projec- 
tion of  one  of  the  sun's  rays  on  that  plane ;  also,  let 
H  I  be  the  scat  of  the  sun  on  the  ichnography,  cut- 
ting the  back  F  G  of  the  elevation  at  I ;  from  I  draw 
I  N  perpendicular  to  I  d,  the  common  intersection  of 
the  ichnography  and  orthography;  from  M,  draw 
M  N  parallel  to  Q  R,  cutting  I  N  at  N ;  tlu-ough  N 
draw  N  O  parallel  to  M  U ;  on  O  as  a  centre,  and 
with  the  distance  O  N,  describe  the  arc  N  R,  cuttijig 


the  side  of  the  recess  at  R ;  through  the  points  S,  V, 
Y,  b,  draw  S  R,  V  U,  Y  X,  and  B  a,  parallel  to  I  d; 
and  through  the  points  Q,  T,  W,  Z,  draw  the  lines 
Q  R,  T  V,  W  X,  and  Z  a,  cutting  the  lines  S  R, 
V  U,  Y  X,  and  B  a,  at  the  points  U,  X,  a;  then 
through  the  points  R,  U,  X,  a,  draw  the  curve 
R  U  X  a,  and  the  line  I  N  R  U  X  a  will  be  the 
edge  of  the  shadow  required. 

PROBLEM  IV. 

Fig.  4.  To  find  the  shadow  of  a  hemisi^here 
niche ;  given  the  seat  and  altitude  of  the 
sun's  rays  on  the  elevation. 

Let  I  N,  G  M,  E  L,  and  C  O  be  liiies  parallel  to 
the  seat  of  the  sun's  rays ;  and  on  these  hues,  as 
diameters,  describe  semicircles  I  K  N,  G  H  M,  and 
E  F  L ;  draw  the  line  A  B,  bisecting  O  C ;  from  any 
of  the  points  C,  E,  G,  I,  as  C,  make  the  angle  O  C  I) 
equal  to  the  sun's  altitude,  cutting  the  side  of  the 
niche  at  D ;  through  the  other  points  E,  G,  I,  draw 
E  F,  G  H,  and  I  K,  parallel  to  C  D,  cutting  the  semi- 
curcles  E  F  G,  G  H  M,  and  I  K  N,  at  the  points 
F  H  K ;  through  the  points  D,  F,  H,  K,  draw  lines 
D  rf,  F  /,  H  //,  and  K  k,  perpendicular  to  the  diam- 
eters, cutting  them  at  the  points  d,  f,  h,  k;  and 
through  the  points  A  k,  h,  /,  d,  draw  a  curve,  which 
will  be  the  edge  of  one  half  of  the  shadow,  from 
which  the  other  half  may  be  drawn,  as  is  shown 
by  the  figure ;  and  this  will  give  the  shadow  com- 
plete. 


OBSERVATIONS. 

I  have  given  one  example  of  the  cflect  of  light  and 
shade  on  mouldings  of  different  curvature :  I  shall 
endeavor  to  show  the  effect  of  light  and  shade  also 
on  many  other  examples,  especially  on  the  five  orders 
of  Architectiue. 

From  what  has  been  said  on  this  subject,  many 
practical  and  useful  rules  in  shadowing  may  be  de- 
duced ;  but  as  I  have  far  exceeded  the  bounds  first 
assigned  for  this  part,  I  must  end  with  observing, 
that,  from  a  consideration  of  the  foregoing  examples, 
the  shadows  of  all  objects,  however  complicated,  may 
be  found,  as  every  object  may  be  considered  as  com- 
pounded of  prisms,  cylinders,  spheres,  and  annuluses ; 


F/<i.2. 

'-'"     ^u:^--^ 

/C ^  ^^ 

il\\ 

1 

■''  z, 

'            ] 

/ 

1  \ 

/ 

\     1 

f' 

/ 

1   / 

/ 

1   / 

/ 

■  /  -■ 

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1  /-' 

U' 

1  \ 

i    \ 

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F 

tr 

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1 

A 

H 

MOULDINGS. 


79 


therefore,  each  part  being  projected  separately,  ac- 
cording to  the  rules  for  its  particular  kind  of  figure, 
the  projection  of  all  the  shadows  in  that  object  will 
be  completed. 

Although  I  have  given  correct  methods  for  shad- 
owing, I  have  no  reason  to  think  that  the  artist  will 
always  be  at  the  trouble  to  project  his  shadows,  for 
as  drawings,  in  general,  are  shadowed  to  an  angle  of 
forty-five  degrees,  and  as  I  have  made  choice  of  that 
angle,  he  will  still  find  these  examples  to  be  his  only 
guide  in  practice,  as  all  the  forms  will  be  sufficiently 


near  when  copied  by  the  eye  and  drawn  by  the  hand 
of  a  judicious  artist. 

Note.  —  The  treatise  on  shadows,  like  the  preceding,  has  not  been 
changed,  but  has  been  inserted  in  the  form  and  manner  in  which 
it  came  from  the  author's  pen.  "Wc  should  have  been  pleased  to 
have  inserted  a  few  plates,  to  elucidate  more  fully  the  effect  of  light 
and  shade  upon  different  objects  ;  but  as  this  could  not  be  done  with- 
out swelling  our  volume  to  a  much  larger  extent  than  was  at  first 
designed,  we  have  given  the  original  as  it  was  in  the  previous  edi- 
tions. For  those  who  may  wish  for  a  more  extensive  knowledge  of 
shadows,  we  would  refer  them  to  Gwilt's  Shades  and  Shadows,  as 
being  one  of  the  clearest  and  most  comprehensive  works  on  the 
subject  with  which  we  have  ever  met.  —  Editoks. 


MOULDINGS. 


Although,  as  observed  in  the  Introduction  of  this  work,  (to  which 
the  student  is  referred,)  the  shaft  of  a  column  may  not  admit  of  any 
ornament  on  its  body,  yet  in  the  base  and  capital  various  ornamen- 
tal parts  are  introduced,  which  are  called  mouldings,  because  they 
are  always  of  the  same  shape,  as  if  they  proceeded  from  the  same 
mould  or  form.  Mouldings  are  generally  di-\-ided  into  Grecian  and 
Roman,  with  reference  to  the  existing  remains  of  the  architecture 
of  those  nations.  The  difference  consists  in  this,  that  the  Romans 
usually  employed  segments  of  circles  in  their  ornaments,  while  the 
Greeks  often  introduced  parts  of  an  ellipsis,  or  some  other  section 
of  a  cone,  varying  from  the  circle. 

The  regular  mouldings  are  variously  disposed  in  different  orders, 
and  may  reasonably  be  supposed  to  have  had  their  origin  in  the  in- 
genuity of  man  rather  than  in  any  essential  necessary  law  in  nature 
or  art.    The  annexed  figure  represents  their  form  and  character. 


~r 


The  fillet,  listel,  annulet,  or  square. 

Astragal,  or  bead. 

Torus,  or  tore. 

Scotia,  trochilus,  mouth,  or  casement. 

Echinus,  ovolo,  or  quarter  round. 

Grecian  echinus. 

Inverted  cj-ma,  talon,  or  ogee. 

C)'ma  recta,  or  cymatium. 

Cavetto,  or  hollow. 


Of  these,  the  Roman  ovolo  and  cavetto  are  never  found  in  Gre- 
cian architecture,  nor  the  Greek  echinus  in  that  of  the  Roman  ■  the 
rest  they  possess  in  common. 


DEFINITIONS. 

1.  Mouldings  are  figures  composed  of  various 
curves  and  straight  lines. 

K  the  mouldings  are  only  composed  of  parts  of  a 
cu-cle  and  straight  lines,  they  are  called  Roman,  be- 
cause the  Romans,  in  their  buildings,  seldom  or 
never  employed  any  other  curve  for  mouldings  than 
that  of  a  circle  ;  but  if  a  moulding  be  made  part  of 
an  ellipsis,  or  a  parabola,  or  a  hyperbola,  the  mould- 
ings are  then  in  the  Grecian  taste. 

Corollary.  —  Hence  it  appears  that  mouldings  in 
the  Greek  taste  are  of  a  much  greater  variety  than 
those  of  the  Roman,  where  only  parts  of  circles  are 
concerned. 

Mouldings  have  various  names,  according  to  the 
manner  in  which  they  are  curved. 

2.  The  straight-lined  part  under  or  above  a  mould- 
ing, in  general,  is  called  a  fillet. 

3.  K  the  contour  of  the  moulding  be  convex,  and 
a  part  of  a  circle,  equal  to  or  less  than  a  quadrant, 
then  the  moulding  is  called  a  Roman  ovolo,  or  an 
echinus,  such  as  Fig.  B,  plate  26. 

4.  If  the  contour  of  the  moidding  be  concave,  and 
equal  to  or  less  than  a  quadrant,  it  is  called  a  cavetto 
or  hollow,  such  as  Fig.  D,  plate  26. 

Corollary.  —  Hence,  a  cavetto  is  just  the  reverse  of 
an  ovolo. 


80 


MOULDINGS. 


5.  A  bead  is  a  moulding,  whose  contour  is  simply 
a  convex  semicircle. 

6.  If  the  contour  be  convex,  and  a  complete  semi- 
circle or  a  semi-ellipsis,  having  a  fillet  above  or  below 
1  he  moulding,  it  is  called  a  torus,  as  Fig.  A,  plate  26. 

Corollary.  —  Hence,  a  torus  is  a  bead  with  a  fillet, 
and  is  more  particularly  distinguished  in  an  assem- 
blage of  mouldings  from  a  bead,  by  its  convex  part 
being  much  greater. 

7.  If  the  contour  of  a  moulding  be  a  concave  semi- 
ellipsis,  it  is  called  a  scotia,  as  Fig.  2,  No.  2,  plate  28. 

8.  If  the  contour  be  convex,  and  not  made  of  any 
part  of  a  circle,  but  of  some  other  of  the  conic  sec- 
tions, having  a  small  bending  inwards  towards  the 
to]j,  the  moulding  is  called  a  Grecian  ovolo  or  echi- 
7ms,  such  as  Fig.  1,  Nos.  1,  3,  3,  4;  Fig.  4,  Nos.  1,  2, 
and  3,  plate  29. 

9.  If  the  contour  be  partly  concave  and  partly 
convex,  the  moulding  in  general  is  called  a  cimatium, 
such  as  Fig.  2,  Nos.  1  and  2 ;  Fig.  8,  Nos.  1  and  2, 
plate  29. 

10.  If  the  concave  parts  of  the  curve  project  be- 
yond the  convex  part,  the  cimatium  is  called  a  cima 
recta ;  such  as  Fig.  2,  Nos.  1,  2,  and  3,  plate  29. 

11.  If  the  convex  part  project  beyond  the  con- 
cave, the  cimatium  is  called  a  cima  reversa  or  ogee, 
as  Fig.  3,  Nos.  1,  2,  and  3,  plate  28. 

12.  The  bending  or  turning  inwards  of  a  small 
part  of  the  convex  curve  of  a  Grecian  moulding  is, 
by  workmen,  called  a  quirk. 


ROMAN     MOULDINGS. 

Plate   26. 

To  describe  an  ovolo  in  the  Roman  taste ;  the 
projections  at  a  and  b  being  given  at  each 
extreme  of  the  curve. 

Figs.  A,  B,  and  C.  Take  the  height  of  the  mould- 
ing ;  on  the  points  a  and  b,  as  centres,  describe  an  arc 
at  c ;  on  c,  as  a  centre,  with  the  radius  c  a  or  c  ft, 
describe  the  arc  a  b,  and  it  will  be  the  contour  of  the 
moulding  required. 

To  describe  a  cavetto,  hanng  the  extremes  of 
the  curve. 
Fig.  D.  The  cavetto  is  described  in  the  same  man- 
ner, but  on  the  opposite  side. 


To  describe  a  hollow,  to  touch  with  two  straight 
lines,  b  d  and  d  a,  one  of  them  at  a  given 
point  a. 

Figs.  E  and  F.  Let  d  be  the  point  of  their  meet- 
ing; make  d  b  on  the  other  line  equal  to  da;  from 
the  points  a  and  b  draw  perpendiculars  to  each  of 
the  lines  d  b  and  d  a,  meeting  at  c ;  on  c,  as  a  centre, 
with  the  radius  c  ft  or  c  a,  describe  an  arc  ft  a,  and  it 
is  done. 

To  describe  a  cima  recta,  the  projections  at  a 
and  b  being  given. 

Fig.  G.  Join  «  ft;  bisect  it  at  e;  then  on  the 
points  a  and  ft  describe  arcs  meeting  each  other  on 
the  opposite  sides  at  c  and  d;  on  the  points  c  and  d, 
with  the  same  radius,  describe  the  opposite  curves 
a  e  and  e  d,  and  it  is  done. 

Fig.  H.  The  cima  reversa  is  described  in  the  same 
manner,  but  in  an  opposite  direction. 


To  describe  a  torus. 


Bisect  the  diameter  at  a ;  on  it,  with  the 
radius,  describe  a  semicircle,  and  it  is  done. 


Fig.  I. 


Fig.  J  is  a  semi-hollow. 
Fig.  K  is  a  bed  mould. 
Fig.  L  is  an  ogee  and  bead. 


GRECIAN  MOULDINGS,  COMPARED  WITH  THOSE  OF 
THE  ROMAN,  TO  SHOW  THE  DIFFERENCE  OF  THEIR 
FORM  AND  APPLICATION. 

L  Of  a  Bead.  —  This  moulding  is  similar  in  both 
Greek  and  Roman  architecture. 

II.  Of  the  Torus.  —  The  torus  in  most  cases  is 
similar  to  a  bead :  it  is  always  so  in  Roman  archi- 
tecture, but  not  always  in  Grecian,  as  may  be  seen 
in  various  examples  where  the  contour  of  the  mould- 
ing is  elliptical.  The  bases  of  the  columns  of  the 
temple  of  Minerva  Polias,  and  also  the  bases  of  the 
columns  on  the  monument  of  Lysicrates,  are  in- 
stances of  the  elliptical  forms  of  toruscs. 

III.  Of  the  Ovolo,  or  Echinus.  —  The  Greek  ovolo 
differs  greatly  from  that  of  the  Roman :  its  contour 
is  generally  a  part  of  the  ellipsis ;  in  some  cases  it  is 
hyperbolical,  and  even  in  some  a  straight  line  ;  the 
elliptical  ovolo  is  always  used  in  cornices,  architraves, 
and  likewise  in  all  mouldings  projecting  from  plain 
surfaces.  It  is  also  to  be  met  with  in  the  capitals  of 
columns. 

Of  such  forms  are  the  echinus  of  the  capitals  of 


I'l .  Hi 


J3©(iffli\RI  EQ®iyiL©[ira©3 


■  / 


(i 

A 

1 

"f 

Vf 

1 

^ 

/ 
/ 

a 

— 5x 

\ 

X 

c 

L. .       " 

MOULDINGS. 


81 


the  Doric  portico  at  Athens,  the  temple  at  Corintii, 
and  the  temple  at  Poestum,  in  Italy,  which  are  all 
elliptical ;  but  the  hyperbolical  form  is  oftcner  to  be 
met  with  in  the  capitals  of  Athenian  buildings  than 
any  other. 

Of  such  arc  the  echinus  of  the  capitals  of  the 
temples  of  Rlinerva  and  Theseus,  and  also  the  capi- 
tals of  the  columns  of  the  Prophylea,  or  gi-and  en- 
trance into  the  citadel.  These  are  all  Athenian 
buildings,  which  were  erected  during  the  administra- 
tion of  Pericles ;  and  the  portico  of  Philip,  King  of 
Macedon,  is  an  instance  in  which  the  echinus  is  in  a 
straight  line. 

Li  Roman  architecture,  the  echinus  is  always 
some  part  of  a  circle,  never  exceeding  a  quadrant, 
but  often  less. 

IV.  Of  the  Cavctlo.  —  The  cavetto  is  the  same 
both  in  Roman  and  Grecian  architecture,  except  in 
its  application.  There  is  not  an  instance  to  be  met 
with  in  Greece  *  where  the  crown  moulding  is  a  ca- 
vetto, but  there  are  many  in  the  Roman. 

V.  0/  the  Doric  Cimatiiun.  —  This  moidding  is 
constantly  used  in  Greek  buildings,  under  the  fillet 
of  a  finishing  or  crown  moulding;  but  in  Roman 
buildings,  there  are  no  instances  whatever  of  any 
such  moulding. 

VI.  Of  the  Cima  Recta.  —  This  moulding  is  nearly 
of  the  same  form,  both  in  the  Grecian  and  Roman 
arcliitecture,  and  is  also  applied  for  the  same  pur- 
pose in  both. 

VII.  Of  the  Cima  Reversa.  —  This  moulding  is 
nearly  similar  in  the  Grecian  and  Roman  architec- 
ture, and  is,  in  general,  applied  under  the  fiUet  of  the 
crown  moulding  of  the  cornices  of  Roman  buildings ; 
but  is  never  so  apjDlied  in  Greek  buildings,  one  in- 
stance excepted,  which  is  the  Portico  of  PliUip,  King 
of  Macedon. 

THE   EFFECT    OF    GRECIAN    MOrLDINGS,    COJIPAHED 
WITH  THE  ROMAN   OF  THE  SAME  KIND. 

I.  Of  the  Ovolo.  —  The  bending  or  turning  in- 
wards of  the  upper  edge  of  the  Grecian  ovolo 
causes,  when  the  sun  shines  on  its  surface,  a  beauti- 
ful variety  of  light  and  shade,  which  gi-catly  relieves 
it  fi-om  plane  surfaces ;  and  if  it  be  entirely  in  shadow, 
but  receive  a  reflected  light,  the  bending  or  turning 

*  There  are  some  out  of  Greece ;  but  of  these  there  are  few  in- 
stances -which  may  not  be  looked  on  as  deviations  from  the  estab- 
lished methods  that  ■were  used  bv  the  Greeks. 

11 


inwards  at  the  top  will  cause  it  to  contain  a  great 
quantity  of  shade  in  that  ])lacc,  but  softened  down- 
wards  round  the  moulding  to  the  under  edge. 

In  the  Roman  ovolo  there  is  no  turning  inwards ;  • 
at  the  top,  therefore,  Avhcn  the  sun  shines  on  its  sur- 
face, it  will  not  be  so  bright  on  its  upper  edge  as  the 
Grecian  ovolo ;  nor  will  it  cause  so  beautiful  a  line 
of  distinction  from  other  mouldings  which  it  is  com- 
bined with  when  it  is  in  shadow,  and  when  lishtcd 
by  reflection. 

II.  Of  the  Cima  Reversa.  —  Li  the  Greek  cima  re- 
versa, the  turning  in  of  its  upper  edge,  and  the  turn- 
ing out  of  its  under  edge,  will  cause  it,  when  the  sun 
shines,  to  be  very  bright  on  these  edges,  which  will 
greatly  relieve  it  from  other  perpendicular  surfaces 
when  combined  together ;  and  when  it  is  in  shadow, 
and  lighted  by  reflection,  the  inclination  of  the  upper 
and  under  edges  will  also  make  a  sti-ong  line  of  dis- 
tinction on  both  edges,  between  it  and  other  mould- 
ings or  planes  connected  with  it ;  whereas  the  upper 
and  under  edges  of  the  Roman  cima  reversa  f  being 
perpendicular  to  the  horizon,  the  lightest  place  on  its 
surface  wiU  not  be  brighter  than  a  perpendicular 
plane  surface,  nor  will  it  be  better  relieved  in  shad- 
ows than  perpendicular  plane  sui'faces  also  in  shadow. 

THE  EFFECT  OF  GRECIAN  MOULDINGS,  COJIPARED 
WITH  ROMAN  MOULDINGS  OF  A  DIFFERENT  KIND, 
BUT  IN  SIMILAR  SITUATIONS. 

I.   Of  the   Greek   Ovolo,  compared  with  the   Roman 
Cavetto,  ivhen  used  as  finishing  Mouldings. 

The  upper  moifldings,  in  all  the  remains  of  anti- 
quity, are  either  entirely  destroyed  or  much  defaced. 
It  is  certain,  that  if  ovolos,  which  are  sti-ong  moiddings, 
had  been  employed  instead  of  cavettos,  \  many  of 
them  would  have  been  almost  entire ;  and  as  the  de- 
grees of  light  and  shade  on  the  surface  of  the  ovolo, 

*  That  is  to  say,  the  upper  edge  of  the  moulding  does  not  recede 
&om  a  plane  touching  its  surface,  and  perpendicular  to  the  horizon. 

t  There  are  some  instances  in  Roman  buildings  where  the  cima 
reversa  is  turned  inwards  at  the  top,  and  outwards  at  the  bottom  ; 
but  this  seldom  occurs,  except  there  is  not  sufficient  projection  to 
its  height. 

X  Some  authors  say,  that  the  cima  recta  and  cavetto  were  always 
used  as  finishing  mouldings  ;  but  it  is  quite  the  reverse  ;  for  in  the 
antique  buildings  now  remaining  in  Greece  there  is  not  a  single 
instance  where  a  cavetto  is  used  for  the  upper  member  of  a  cornice ; 
but  in  Doric  buildings,  the  cornice  always  finishes  with  an  ovolo ; 
and  in  buildings  of  the  Ionic  and  Corinthian  orders,  they  are  fin- 
ished with  cima  rectas. 


82 


MOULDINGS. 


whether  firom  sunshine  or  from  any  other  light,  is 
beautiful  and  soft,  the  shadow  of  the  cavetto  from 
sunshine  is  very  hard,  and  will  not  contain  so  great 
a  variety  of  light  and  shade  on  its  surface ;  it  will, 
therefore,  be  less  pleasing  to  the  eye. 

II.     The  Doric  Cimatium  used  hj  the  Grecians  under 
the  Fillet  of  the  Croicn  Moidding,  compared  tvilh 
the  Cima  Reversa  in  the  same  Situation. 
The  front  of  the  Doric  cimatium  is  a  convex  ellipti- 
cal curve,  and  is  sunk  at  the  upper  edge  in  the  manner 
of  a  Grecian  ovolo ;  therefore,  tlie  light  and  shade  on 
its  front  will  be  nearly  similar  to  an  ovolo ;  and  as 
the  sinking  upwards  behind  the  front  will  cause  it 
to  contain  a  quantity  of  shade,  —  which  will  form  a 
line  of  separation  from  the  corona,  and,  consequent- 
ly, make  it  appear  more  distinct  at  a  distance,  but 
the  Roman  cima  reversa,  being  so  very  flat,  would 
not  be  well  relieved,  —  its  profile  would  be  lost  en- 
tirely at  a  distance. 


MODERN     MOULDINGS. 

I  have  given  several  modern  designs  for  mould- 
ings, not  that  in  my  own  opinion  they  are  more 
tasteful  than  the  Grecian  or  Roman,  but  that  by  com- 
bining them  it  affords  a  greater  variety ;  and,  as  some 
are  fond  of  new  things,  they  may  be  preferred. 
Plate  27. 

A  is  a  cima  recta.  B  is  a  cima  reversa,  or  ogee. 
C  is  a  bed  mould.  These  differ  from  the  Roman 
only  in  their  curves  being  more  graceful,  but  are 
formed  on  the  same  principle. 

D,  E,  F,  G,  II,  I,  J,  K,  and  L  are  formed  on  the 
principle  of  the  Grecian,  with  a  slight  alteration  in 
their  curves. 


GRECIAN     MOULDINGS. 
Plate  29. 

To  describe  the  Grecian  echinus  or  ovolo ;  the 
tangent  A  B,  at  the  bottom,  the  point  of  con- 
tact A,  and  the  greatest  projection  of  the 
moulding  at  C  being  given. 

Fig.  4,  No.  2.   From  A,  draw  A  D  E  perpendicu- 


lar ;  tlirough  C  draw  C  D  parallel  to  the  tangent 
B  A,  cutting  A  E  at  D ;  make  D  E  equal  to  A  D 
then  v.'ill  D  be  the  centre  of  an  ellipsis,  and  C  D  and 
D  A  will  be  two  semi-conjugate  diameters,  from 
wliich  the  ellipsis  may  be  described  by  plate  6,  Ge- 
ometry. 

Fig.  4,  No.  1.  This  figure  is  described  in  the  same 
manner,  and  shows  a  greater  projection,  the  tangent 
being  also  taken  in  a  higher  position. 

The  same  things  being  given,  to  describe  the 
moulding  nearly,  when  the  point  of  contact  A 
is  at  the  extremity  of  the  transverse  axis. 

Fig.  4,  No.  3.  From  A,  draw  A  D  E  perpendicular 
to  the  tangent  B  A ;  parallel  to  it  draw  C  G,  cutting 
the  tangent  A  B  at  G ;  also,  through  C  draw  C  D 
parallel  to  the  tangent  A  B,  cutting  A  D  E  at  D,  the 
centre  of  the  ellipsis,  for  which  D  C  and  D  A  are  the 
semi-transverse  and  semi-conjugate  axis,  and  pro- 
ceed as  before. 

Plate  2S. 

The   semi-transverse    and    semi-conjugate    axis 
being  given,  to  describe  the  moulding. 

Fig.  1,  Nos.  2  and  3.  Proceed  as  in  plate  6,  Ge- 
ometry, and  you  will  have  the  contour  of  the  mould- 
ing required. 

To  describe  the  cima  recta,  the  perpendicular 
height,  II  L,  being  given,  and  its  projection, 
L  I. 

Fig.  2,  No.  1.  Complete  the  rectangle  I  L  H  F, 
and  divide  the  whole  rectangle  into  four  equal  rec- 
tangles ;  then  inscribe  the  concave  quadrant  of  an 
ellipsis  in  the  rectangle  I  K  C  B,  and  a  convex  quad- 
rant in  the  rectangle  C  G  H  D,  and  it  is  done. 

To  describe  a  cima  reversa,  the  point  A  being 
nearly  the  greatest  projection  at  the  top ;  D 
the  extremity  of  the  curve  at  the  bottom ; 
and  D  C  a  line  parallel  to  a  tangent,  at  the 
point  of  junction  of  the  opposite  curve. 

Fig.  3,  No.  3.  Draw  A  C  at  right  angles  to  C  D, 
cutting  C  D  at  C,  and  complete  the  rectangle  A  C  D  E ; 
then  proceed  as  before,  but  in  a  contrary  direction, 
and  you  will  have  tlie  contour  required. 


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THE     ORDERS. 


83 


To  describe   an   echinus  having   the  depth  of 
the   moulding  C  D,  the   greatest   projection 
at   D,   and    to   be    quirked   at   the    top    and 
bottom. 
Fig.  2,  No.  3.    Complete  the  rectangle  C  B  A,  and 

proceed  as  in  plate  6,  Geometry. 

To  describe  a  scotia. 
Fig.  2,  No.  2.  Join  the  ends  of  each  fillet  by  the 
right  line  A  B  ;  bisect  A  B  at  D ;  through  D  draw 
C  D  E  parallel  to  the  fillets,  and  make  C  D  and  D  E 
equal  to  the  depth  of  the  seotia ;  then  will  A  B  be  a 
diameter  of  an  ellipsis,  and  C  E  its  conjugate.  Pro- 
ceed as  in  plate  6,  Geometry. 

How  to  describe  Grecian  mouldings,  whether 
elliptical,  parabolical,  or  hyperbolical  ;  the 
greatest  projection  at  B  being  given,  and 
the  tangent  C  F  at  F,  the  bottom  of  the 
moulding. 
Fig.  4,  Nos.  1,  2,  and  3.   Draw  G  F  a  continuation 

of  the  upper  side  of  the  under  fillet ;  through  B  draw 


B  G  perpendicular  to  B  F,  cutting  it  at  G,  and  the 
tangent  F  C  at  the  pohit  C ;  also,  through  B  draw 
B  E  parallel  to  G  F ;  and  through  F  draw  F  D  E  A 
parallel  to  G  B,  cutting  B  E  at  E ;  make  E  A  equal 
to  E  F,  E  D  equal  to  C  G,  and  join  B  D  ;  then  divide 
each  of  the  lines  B  D  and  B  C  into  a  like  number 
of  equal  parts ;  from  the  point  A.,  and  through  the 
points  1,  2,  3, 4,  in  B  C,  draw  lines,  cutting  the  former, 
which  will  give  the  points  in  the  curve. 

If  the  point  C,  where  the  tangent  cuts  the  line  B  G, 
be  less  than  one  half  of  B  G,  from  G  the  moulding 
will  be  elliptical,  as  in  Fig.  4,  No.  2. 

K  G  C  be  one  half  of  B  G,  then  the  moulding  is 
parabolical,  as  in  Fig.  4,  No.  1. 

If  G  C  be  gi-eater  than  half  of  B  G,  then  the  mould- 
ing is  hyperboLieal,  as  in  Fig.  4,  No.  3. 

By  this  means  you  may  make  a  moulding  to  any 
form  you  please,  whether  flat  or  round. 

[On  plate  30  will  be  found  four  designs  for  archi- 
traves, for  the  finish  of  doors  and  windows,  full  size. 
These  are  substituted  for  plates  83  and  84  of  the  last 
edition,  as  being  more  in  keeping  with  the  taste  of 
the  times,  &c.  —  Editors.] 


THE    OEDERS. 


The  term  order  seems  to  sustain  the  same  relation 
to  architecture  that  the  term  harmony  does  to  music, 
or  the  ancient  term  ordonnancc  to  painting.  It  is,  in 
fact,  no  more  nor  less  than  an  assemblage  of  parts 
and  mouldings,  so  disposed  as  to  give  an  effect 
at  once  pleasing  to  the  eye,  and  proportioned  and 
adapted  to  the  ofiice  each  has  to  perform. 

Vitruvius,  who  was  nearly,  if  not  the  first  writer 
on  architecture  who  flourished  in  the  first  century 
after  the  birth  of  Christ,  expresses  the  idea  as  fol- 
lows :  "  It  is  an  apt  and  regular  disposition  of  the 
members  of  a  work  separately,  and  a  comparison  of 
the  universal  proportion  with  symmetry."  This,  in 
his  work,  (chapter  2d,)  he  calls  ordonnancc.  Scamozzi, 
the  son  of  an  architect,  and  himself  one  of  the  old 
masters,  the  rival  of  Palladio,  and  who  after  the  death 
of  that  artist,  in  1580,  had  no  competitor,  is,  we  be- 
lieve, the  first  of  the  ancient  \%Titers  that  has  given 


us  what  may  be  termed  the  description  of  an  order. 
He  observes  in  his  book,  (2d  chapter,  2d  part,)  "  that 
it  is  a  kind  of  excellency  which  infinitely  adds  to  the 
shape  and  beauty  of  buildings,  sacred  or  profane." 
He  seems  to  have  attempted  to  convey  the  same  idea 
as  the  author  before  quoted,  which  idea  is  compre- 
hended in  the  terms  propriety  and  harmony.  Having 
now  given  the  idea  which  the  ancients  would  seem 
to  have  us  entertain  by  the  Latin  word  order,  we  wUl 
proceed  to  illustrate  more  fully  the  composition  and 
use  of  the  orders.  First,  then,  an  order  is  composed 
of  two  parts,  viz.,  the  column  and  the  entablature ; 
these  are  again  each  divided  into  three  other  parts, 
which  parts  are  composed  of  an  assemblage  of  mould- 
ings, each  respectively  proportioned  and  adapted  to 
the  order  of  which  it  is  a  part.  The  parts  of  the  entab- 
lature are  called  the  architrave,  frieze,  and  cornice ; 
those  of  the  column  are  the  base,  shaft,  and  capital,  as 


84 


THE    ORDERS. 


may  be  seen  on  plate  50.  These  are  again  subdivided 
into  other  parts,  as  will  be  seen  by  the  description 
of  the  respective  orders.  The  species  of  orders  are 
five  in  number  —  the  Tuscan,  Doric,  Ionic,  Corin- 
thian, and  Composite ;  each  is  a  composition  peculiar 
to  itself,  and  is  calculated  to  produce  the  expression 
it  is  intended  to  possess,  viz.,  strength,  grace,  ele- 
gance, and  richness.  The  orders  above  named  rightly 
understood,  and  correctly  applied,  are  the  foundation 
upon  which  architecture  has  long  rested  as  an  art. 
The  oldest  of  these  is  the  Doric,  the  next  the  Ionic, 
and  the  last  the  Corinthian.  The  Tuscan  is  said  to 
have  been  invented  by  the  inhabitants  of  Tuscany ; 
and  Vitruvius  has  first  given  it  a  name  and  placed 
it  in  his  book,  a  copy  of  which  is  shown  on  page  31 ; 
but  he  docs  not  inform  us  of  a  single  building  on 
which  it  has  been  employed,  and  as  no  examples 
exist  to  warrant  the  belief  of  its  frequent  use  in  his 
day,  we  are  led  to  suppose  that  its  rustic  plainness 
did  not  suit  the  Roman  taste  of  his  time.  It  has, 
however,  received  the  approbation  of  the  principal 
masters  who  have  succeeded  him,  and  is  now  ranked 
with  the  regular  orders.  The  Composite  is  a  Roman 
invention,  and  has  been  termed  by  Sii'  Henry  Wotton, 
in  his  Parallel  of  Ancient  Architecture  with  the  Mod- 
ern, the  compounded  order.  It  is  composed  of  parts 
of  the  other  orders,  but  principally  of  the  Ionic  and 
Corinthian.  The  proportion  of  the  parts  of  the  or- 
ders are  as  various  as  the  examples  —  no  two  authors 
agreeing.  In  the  examples  given,  the  parts  are  fig- 
ured, as  will  be  seen  ;  and  the  proportion  assigned  to 
each,  as  the  example  or  author  has  directed  explana- 
tions of  the  orders  more  in  detail,  will  be  found  at- 
tached to  them  under  their  respective  heads.  —  Eds. 


TUSCAN     ORDER. 

The  Komans  added  the  Tuscan,  or  Etruscan,  to  the  tlncc  Grecian 
orders,  as  they  subsequently  did  the  Composite.  The  idea  of  the 
Tuscan  is  undoubtedly  derived  from  the  Doric  order,  from  ■which  it 
differs,  according  to  the  view  taken  of  it  by  Aldrich,  as  much  as  the 
appearance  of  an  inhabitant  of  the  country  does  from  one  of  a  cit}'. 
There  is  extant  no  ancient  specimen  of  it  with  an  entablature.  It  is  the 
first  of  the  Italic  orders,  and  is  called  Tuscan,  as  having  been  origi- 
nally employed  by  that  ancient  people,  once  powerful  in  Italy. 
"  Vitruvius  speaks  of  it  as  rustic  even  to  deformit)' ;  nor  were  the 
later  masters  more  favorable  to  it,  except  Palladio."  Having  no 
complete  exaraide  from  antique  buildings,  that  which  is  given  in 
this  work  is  taken  from  the  description  by  Vitruvius. 


Plate  31. 

From  Vitruvius,  tvith  lite  Proporlion  of  the  Parts  in 
Numbers. 

A^'e  have  no  complete  example  of  this  order  re- 
maining from  antique  buildings ;  and  all  that  we 
know  of  it  is  from  the  description  by  Vitruvius,  from 
which  this  example  is  taken,  and  is,  therefore,  the  only 
standard. 

The  proportions  of  the  parts  are  exhibited  by  equal 
divisions  on  the  plate. 

That  celebrated  building,  St.  Paul's,  Covent  Gar- 
den, is  the  only  true  specimen  there  is  of  the  Tuscan 
order  in  England.  It  may  be  adapted  with  great 
propriety  to  market-places,  as  the  simplicity  of  its 
parts  and  the  extraordinary  projection  of  the  cornice 
render  it  suitable  for  that  purpose. 

Fig.   1.  Elevation  of  the  order,  from  Vitruvius. 

Fig.  2.  The  ichnography  of  the  mutulcs  in  the 
cornice. 

Fig.   3.  Profile  of  the  upper  part  of  the  cornice. 

The  column  is  seven  diameters  high ;  the  base  and 
capital  are  each  half  a  diameter ;  the  base  is  divided 
into  two  equal  parts,  one  of  which  is  given  to  the 
plinth,  the  other  to  the  torus  and  fillet ;  divide  the 
capital  into  three  equal  parts,  give  one  to  the  hypo- 
traehelion,  one  to  the  ovolo  and  fillet,  and  the  upper 
one  to  the  abacus.  The  mutulcs  in  the  cornice  are 
to  project  one  fourth  of  the  length  of  the  column. 

Fig.  4.  A  modern  example  of  the  Tuscan  order, 
with  the  proportional  measm'es  in  numbers. 

On  plate  32,  we  have  given  a  design  for  the  regu- 
lar Tuscan  order.  No  example,  except  that  on  plate 
31,  is  in  any  of  the  previous  editions.  The  design 
here  given  is  a  composition  from  Chambers  and  Pal- 
ladio. In  his  example  of  the  Tuscan,  Chambers  has 
followed  Vignola  and  Serlio,  in  omitting  the  break 
in  the  architrave,  and  making  it  consist  of  only  two 
members.  This,  it  is  acknowledged,  is  according  to 
the  example  given  us  by  Vitruvius  ;  but  as  liberty 
has  been  taken  to  adapt  it  to  other  times,  there  seems 
to  be  no  excuse  why  the  method  pursued  by  Palladio 
should  not  be  entitled  to  as  much  attention  as  that 
by  Vignola.  The  majority  of  authors  have  approved 
the  practice  of  the  former ;  in  the  example  we  have 
composed,  we  have  retained  the  bold  and  classic  pro- 
portions, as  given  by  Chambers,  for  the  cornice,  add- 
ing to  it  the  architrave  by  Palladio.  The  column 
is  according  to  that  given  us  by  Chambers,  and  it  is, 
we  believe,  the  most  approved  proportion  with  which 


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THE    ORDERS, 


85 


we  are  acquainted.  No.  1,  on  plate  32,  is  the  order 
figured  to  a  scale  of  minutes.  No.  2  is  the  impost 
and  archivolt  of  the  same.  —  Editors. 


ROMAN    DORIC. 

Some  architects  have  maintained  that  the  Doric  order  h  unfit  for 
sacred  edifices,  by  reason  of  its  irregularity.  This  opinion  was  held 
by  Tarchesius,  Pytheus,  and  Ilermogenus.  The  latter,  after  having 
prepared  marble  materials  for  building  a  Doric  temple,  changed  the 
order,  and  made  it  Ionic,  dedicating  it  to  Bacchus.  The  Doric  or- 
der, however,  is  not  deficient  in  grandeur,  but  an  inconvenience 
arises  in  the  distribution  of  the  triglyplis  and  lacunaria ;  for  it  is 
necessary  that  the  triglyphs  should  bo  placed  over  the  middle  quar- 
ters of  the  columns,  .md  the  metopes,  which  are  between  the  tri- 
glyphs, must  be  as  long  as  high;  also,  the  triglyphs  at  the  angles  are 
placed  at  the  extremities,  and  not  over  the  middle  of  the  columns ; 
therefore,  the  metopes  which  are  next  the  angular  triglyphs  will 
not  be  square,  but  longer  by  half  the  breadth  of  a  trigljqih.  Some, 
who  wish  to  make  the  metopes  equal,  lessen  the  extreme  inter- 
columniation  by  half  the  breadth  of  the  triglyph.  However,  the 
metope  or  the  contracting  of  the  intercolumniatiou  is  a  defect. 
Though  the  ancients  have  been  observed  to  neglect  exact  regularity 
in  Doric  buildmgs,  it  is  shown  in  its  proper  place  how  far  we  ought 
to  follow  our  masters. 


The  front  of  a  Doric  temple,  where  the  columns 
are  placed,  is  divided,  if  it  be  terastyle,  into  twen- 
tj'-eight  parts  ;  if  hexastyle,  into  forty-four.  One  of 
these  parts  will  be  the  module,  which,  in  Greek,  is 
called  Embafcs,  and  by  which  all  the  other  parts  are 
proportioned. 

The  thickness  of  the  column  must  be  tw^o  mod- 
ules ;  the  height,  with  the  capital,  fourteen ;  the 
height  of  the  capital  one  module,  the  breadth  two 
modules  and  a  sixth.  The  height  of  the  capital  is 
divided  into  three  parts,  of  which  one  is  given  to  the 
abacus,  with  the  cimatium ;  another  to  the  echinus, 
with  the  annulets ;  and  the  third  to  the  hypotra- 
chelion.  The  columns  are  diminished  as  described 
on  the  plates. 

The  height  of  the  epistilium,  with  the  tenia  and 
drops,  is  one  module.  The  tenia  has  the  seventh  of 
a  module,  the  length  of  a  gvittse  under  the  tenia 
coinciding  with  the  perpendicular  of  the  triglyphs. 
Their  height  with  the  regula  is  one  sixth  of  a 
module.  The  breadth  of  the  epistilium  also  answers 
to  the  hypotrachelion  of  the  column. 

On  the  epistilium  are  placed  the  triglyphs  with 
the  metopes,  having  the  height  of  one  module  and  a 


half,  and  the  breadth  in  front  one  module.  They 
must  be  so  distributed  that  they  may  be  over  the 
centre  of  tlie  columns  at  the  angles,  and  two  be- 
tween each  column.  The  breadth  of  the  triglyphs 
is  divided  into  twelve  equal  parts,  of  which  tlie 
breadth  of  the  femur  in  the  middle  will  be  two  parts ; 
then  a  channel  is  cut  on  each  side  of  the  femur,  the 
breadth  of  each  channel  being  equal  to  two  parts. 
Next  to  the  channels  two  other  femurs  are  left,  one 
on  the  right  and  the  other  on  the  left,  each  equal  to 
the  breadth  of  the  middle  femur,  or  two  parts ;  then 
a  part  will  remain  next  to  the  edge  of  each  triglyph, 
which  is  to  be  cut  away  in  the  form  of  a  semi- 
channel.  On  either  side  of  this  channels  are  sunk, 
as  if  imprinted  by  the  elbow  of  a  square.  To  the 
right  and  left  of  these  another  femur  is  formed.  In 
the  same  manner,  semi-channels  must  be  sunk  at  the 
extremities.  The  triglyphs  being  thus  disposed,  the 
metopes  are  as  high  as  long;  on  the  angles,  also,  the 
semi-metopes  are  made  half  a  module  in  width. 

Thus  all  the  errors  arising  from  the  wrong  disti-i- 
bution  of  the  metopes,  intcrcolumniations,  and  lacu- 
naria will  be  rectified. 

The  capitals  of  the  triglyphs  must  have  one  sixth 
of  a  module.  On  these  capitals  is  placed  the  coro- 
na, projecting  a  half  and  a  sixth  part  of  a  modiUe, 
having  a  Doric  cimatium  below,  and  another  above. 
The  corona,  with  the  cimatiums,  are  half  a  module 
in  thickness.  In  the  under  part  of  the  corona,  per- 
pendicularly over  the  ti-iglyphs  and  metopes,  the 
guttse  in  the  mutules  are  so  distributed  that  there 
may  be  six  in  length,  and  three  in  breadth.  The 
spaces  between  the  metopes  being  rather  broader 
than  the  triglyphs,  are  either  left  plain,  or  carved ; 
and  at  the  edge  of  the  corona  a  channel  is  cut, 
called  Scotia;  all  the  remainder,  as  the  tympanum, 
the  cima,  and  corona,  are  the  same  as  in  the  Ionic 
order. 

Concerning  the  diminution  of  the  column,  accord- 
ing to  Vitruvius,  he  gave  the  following  rule  for  all 
kinds  of  columns,  the  Tuscan  excepted  :  — 

The  diminution  of  the  top  of  the  column  at  the 
hypoh-achelion  is  thus  regulated :  If  the  column  be 
not  less  than  fifteen  feet  high,  the  thickness  at  the 
bottom  is  divided  into  sis  parts,  and  five  of  these 
parts  are  given  as  the  thickness  at  the  top. 

"  If  the  height  is  from  fifteen  to  twenty  feet,  the 
bottom  of  the  shaft  is  divided  into  six  parts  and  a 
half,  and  five  and  a  half  of  these  parts  make  the 


86 


THE    OKDEKS. 


thickness  of  the  column  at  top ;  and  if  from  twenty 
to  thirty  feet,  the  bottom  is  divided  into  seven  parts, 
and  six  of  these  make  the  diminution  at  the  top. 
If  it  is  from  thirty  to  forty  feet  high ;  the  bottom 
thickness  is  divided  into  seven  parts  and  a  half,  of 
which  six  and  a  half  is  the  measure  of  the  diminu- 
tion at  the  top.  If  from  forty  to  fifty  feet,  it  is 
divided  into  eight  parts,  whereof  seven  will  make 
the  thickness  of  the  hypotrachelion  at  the  top  of  the 
shaft.  And  if  it  is  still  higher,  the  same  propor- 
tional method  is  observed ;  for,  as  a  greater  height 
causes  them  to  appear  more  diminished,  they  are, 
therefore,  to  be  corrected  by  an  addition  of  thickness, 
beauty  being  the  provmcc  of  the  eye,  which,  if  not 
satisfied  by  the  due  proportion  and  augmentation  of 
the  members,  con-ccting  apparent  deficiencies  with 
proper  additions,  the  aspect  will  appear  coarse  and 
displeasing. 

Plate   33. 

This   plate  shows   the   elevation   of  the    Roman 
Doric,  as  given  by  Palladio. 
Fig.  1.  The  elevation. 
Fig.  2.  The  cornice  inverted. 
Fig.  3.  The  capital  inverted. 

Plate  34. 

Elevation  of  the  Doric  Order  from  the  Baths  of  Bio- 
clesian,  at  Rome,  with  the  Proportions  in  Numbers. 

The  cornice  of  this  example  is  not  Doric  ;  it  is  too 
abundant  with  mouldings,  and  overcharged  with 
enrichments. 

The  disposition  of  the  triglyphs  and  metopes  in 
the  fi-ieze  is  according  to  the  rules  of  Vitruvius. 

The  capital  is  not  Doric,  but  of  another  kind ;  nor 
could  this  composition  be  known  to  have  the  least 
resemblance  to  the  Doric  order,  if  the  triglyphs  in 
the  frieze  were  omitted. 

Fig.  1.  The  elevation  of  this  example. 

Fig.  2.  A  section  of  the  column,  showing  the 
flutes. 


ROMAN    IONIC, 
Plate   35, 

Is  the  Roman  Ionic  as  approved  by  Chambers, 
and  is  inserted  to  supply  the  place  of  plates  56  and 
57   of   the   previous   edition,   which   contained  the 


example  of  the  Temple  of  Concord,  at  Rome.  This 
was  a  very  singular  example,  which  was,  perhaps, 
the  best  authority  the  author  had  for  introducing  it. 
The  cornice  contains  mutulcs  resembling  the  Doric, 
and  dentils  as  in  the  Ionic.  The  frieze  and  archi- 
trave are  plain,  with  the  exception  of  two  breaks, 
the  top  one  of  which  contains  a  cavetto  or  hol- 
low. There  is  no  band  moulding  to  separate  the 
firieze  from  the  architrave.  The  capital  is  angular, 
volutcd,  and  is  not  without  merit ;  but  the  extreme 
plainness  of  the  space  between  the  cornice  and  the 
top  of  the  capital,  and  the  connection  between  the 
cornice  and  frieze,  is  so  inelegant,  that  the  anath- 
emas of  those  who  would  have  used  it  have  been 
called  down  upon  it,  and  it  is  now  scarcely  if  ever 
used.  The  example  given  by  Chambers  is,  perhaps, 
as  good  as  any  wc  have ;  and  we  have,  therefore,  in- 
serted it  to  complete  the  Roman  orders.  Fig.  1  is 
the  order,  and  figs.  2,  3,  and  4  the  details  of  the  cap- 
ital. —  Editors. 


CORINTHIAN    ORDER. 

The  Corinthian  order  took  its  rise  in  the  flourishing  days  of 
Corinth,  a  celebrated  city  commanding  the  communication  of  the 
peninsula  of  Feloponncsus  with  the  continent  of  Greece.  It  is 
generally  regarded  by  writers  on  architecture  as  being  more  delicate 
than  the  Ionic,  and  is  thought  to  resemble  the  graceful  figure  of  a 
virgin.  Among  the  ancients,  it  had  much  resemblance  to  the  Ionic. 
According  to  Vitruvius,  it  imitated  that  order  in  every  part  but  in 
the  capital  of  the  pillar.  In  the  introduction  to  this  work,  we  have 
alluded  to  the  pretty  Greek  story  told  of  the  origin  of  the  capital. 
Villapandus  gives  another  equally  dubious  account  of  its  origin ;  and 
Aldrich  conjectures  as  more  probable  that,  as  the  shaft  of  a  pillar 
represents  the  trunk  of  a  tree,  so  the  tree  being  lopped,  and  sprout- 
ing again,  furnished  the  hint  for  the  design  of  this  capital.  But, 
however  this  may  be,  wc  believe  it  will  be  generally  conceded  that, 
in  attempting  too  much,  this  order  has  deviated  firom  the  true  sim- 
plicity of  nature.  It  marked  an  age  of  luxury  and  magnificence, 
when  pomp  and  splendor  had  become  the  predominant  passion,  but 
had  not  yet  extinguished  the  taste  for  the  sublime  and  beautiful; 
and  in  this,  attempts  were  made  to  unite  these  characters. 


DEFINITIONS. 

1.  An  order  which  has  two  annular  rows  of  leaves 
in  the  capital,  each  leaf  of  the  upper  row  growing 
between  those  of  the  lower  row,  in  such  a  manner 
that  a  leaf  of  the  upper  row  may  be  in  the  middle 
of  each  side  or  face  of  the  capital,  —  and  if  between 


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THE    ORDERS. 


87 


each  space  of  the  upper  leaves  there  spring  stalks 
with  volutes,  two  of  which  meet  at  the  angles  of  the 
abacus,  and  two  in  the  middle  of  the  capital,  either 
touching  or  interwoven  with  each  other,  —  a  capital 
so  constructed  is  called  Corinthian. 

2.  An  order  wliich  has  a  Corinthian  capital,  and 
an  Ionic  or  any  other  entablature,  is  called  the  Corin- 
thian order. 

Plate  38. 

The  Corinthian   Order,  from  the  Pantheon,  at  Rome. 

This  example,  though  plain,  is  yet  beautiful  and 
chaste,  and  is  an  excellent  model  of  the  order. 

Fig.  1.  Elevation  of  the  order  in  numbers. 

Fig.  2.  Section  of  one  quarter  of  the  column  next 
the  capital ;  also  a  section  of  one  quarter  of  the  col- 
umn next  the  base. 


Fig. 


Elevation  of  the  base  of  a  larger  size. 


Plate  37. 


Fig.  1.  Is  the  outline  of  the  leaves  and  elevation 
of  the  capital,  from  the  Pantheon,  as  shown  in 
plate  38. 

Fig.  2.  The  capital  inverted,  showing  an  angle  of 
the  architrave. 

Fig.  3.  The  elevation  of  a  leaf  in  the  same. 

Fig.  4.  The  elevation  of  a  leaf  in  the  capital  of  a 
column,  Ixom  the  Temple  of  Jupiter  Stator,  at  Rome. 

Fig.  5.  The  side  elevation  of  the  modiUion,  from 
the  Temple  of  Jupiter. 

Fig.  6.  The  modillion  inverted. 

Plate  36. 

From  the  three  Columns  in  the  Campo  Vaccina,  sup- 
posed to  be  the  Remains  of  the  Temple  of  Jupiter 
Stator,  at  Rome. 

The  engi'aving  exhibited  in  this  plate,  of  that  cel- 
ebrated example  of  the  remains  of  Jupiter  Stator,  is 
as  accurate  as  any  yet  published:  the  capital  and 
entablature  are  restored  from  the  drawings  of  an 
artist,  who  was  so  obliging  as  to  favor  me  with 
sketches  of  the  ornament  which  he  had  from  the 
original.  The  elegance  and  beauty  of  the  capital, 
its  graceful  form,  the  grandeur  and  excellent  propor- 
tion of  the  entablature,  wdth  the  delicacy  of  the  or- 
nament, render  this  one  of  the  most  complete  exam- 
ples now  existing  of  the  Corinthian  order. 

Fiff.  1.  Elevation  of  the  order  in  numbers. 


Fig. 


The  cornice  inverted,  showing  the  enrich- 


ments of  the  modillions  and  mouldings. 


COMPOSITE     ORDER. 

The  second  Italian  order,  and  last  of  the  five  orders  of  architec- 
ture, is  the  Composite  ;  which  some  -writers  have  divided  into  three 
species,  or  orders.  The  first,  called  the  Composite,  is  composed  of 
the  Ionic  and  Corinthian,  "  which  two  esliibit  more  graces  in  com- 
bination than  either  of  them  would  if  joined  with  the  Doric.  The 
Composite  is  more  slender  than  the  Corinthian,  and  more  ornamented 
with  sculpture  ;  if  the  latter  bears  any  resemblance  to  a  young  maid, 
the  former  represents  an  harlot." 

The  second  species,  as  given  by  Aldiich  and  Smyth,  is  "  Dorico- 
lonic  ;  the  only  remaining  instance  of  which  may  be  seen  at  Home, 
in  the  ruins  of  the  Temple  of  Concord.  The  base  of  the  column  is 
Attico-Ionic,  and  without  a  plinth,  except  in  angular  pillars.  The 
capital  is  lonico-Doric,  with  the  volutes  projecting,  as  in  the  Italian ; 
the  abacus  is  Corinthian  ;  the  frieze  is  sculptured,  but  the  larmier 
is  plain.     It  has  a  beautiful  appearance." 

The  third  species  of  Composite  is  where  the  column  is  of  one 
order,  and  the  entablature  of  another ;  for  instance,  when  the  col- 
umn is  Corinthian,  and  the  entablature  Doric ;  in  which  case,  it 
would,  therefore,  be  very  properly  termed  Dorico-Corinthian.  "  This 
is  approved  of  even  by  Vitruvius  ;  and,  in  fact,  was  introduced  into 
the  Temple  of  Solomon,  whose  columns  were  Corinthian,  supporting 
a  Doric  entablature." 

The  Romans  first  introduced  the  Composite  order  into  their  tri- 
umphal arches,  to  show  their  dominion  over  the  people  whom  they 
conquered. 


Of  this  order  we  have  many  examples  from  the 
ancients ;  but  the  following  is  the  most  celebrated : 
it  is  taken  from  the  Arch  of  Titus,  which  was  executed 
soon  after  the  destruction  of  Jerusalem,  in  order  to 
commemorate  that  remarkable  event. 

Plate  39. 

From  the  Arch  of  Titus,  at  Rome. 
This  most  beautiful  and  elegant  example  is  made 
choice  of  as  the  most  proper  model  for  this  order. 

TABLE, 

Showing  the  relative  Proportions  of  Grecian  Doric 
Columns  contained  in  this   Work. 


Names  of  Buildings. 

Colmnns. 

Capital. 

Architrave. 

Frieze,  i  Cornice. 

Modules.  Min. 

Minutes. 

Minutes. 

Minutes.  Minutes. 

Portico  of  Philip,  K.  of  Macedon 

The  Temple  of  Theseus 

The  Temple  of  Minerva 

13     21^ 
11   12i 

11  4 

12  2i 

4i 
30J. 
27^ 
21f 
20^ 

38 

50 

43i 

40 

37 

44 

48 
43i 
42i 
35 

25 
32 

23A 

21 A 
25 

Found  in  Asia,  near  the  Tem-  ( 
pie  of  M  inerva  Polias \ 

88 


PILASTERS, 


PILASTERS. 

Pilasters  are,  it  is  believed,  a  Roman  invention,  and  certainly  an 
improvement.  The  Greeks  cmiiloyed  anta;  in  their  temiiles,  to  re- 
ceive the  architraves  -nliere  they  entered  upon  the  walls  of  the  cell. 
Tlicsc,  though  they  were,  in  one  direction,  of  equal  diameter  with 
the  columns  of  the  front,  were  in  flank  extravagantly  thin  in  pro- 
portion to  their  height,  and  neitlier  their  bases  nor  capitals  bore  any 
resemblance  to  those  of  tlie  columns  they  accompanied.  The  Ro- 
man artists,  disgusted,  probably,  with  the  meagre  aspect  of  these 
antx,  and  the  want  of  accord  in  their  bases  and  capitals,  substituted 
pilasters  in  theii-  stead,  which,  being  proportioned  and  decorated  in 
the  same  manner  mtli  the  eolumns,-arc  certainly  more  seemly,  and 
preserve  the  unity  of  the  composition  much  better.  The  reader  will 
find  some  additional,  and  perhaps  not  unimportant,  remarks  iu  re- 
lation to  the  pilaster  in  tlie  introduction  to  this  work. 


Pilasters  differ  from  columns  in  their  plan  only, 
whicli  is  square,  while  that  of  the  column  is  round. 
Their  bases,  capitals,  and  entablatures  have  the  same 
parts,  with  all  the  same  heights  and  projections,  as 
those  of  columns ;  and  they  are  distinguished  in  the 
same  manner,  by  the  names  of  Tuscan,  Doric,  Ionic, 
Corinthian,  and  Composite.  Of  the  two,  the  col- 
umn is  doubtless  most  perfect.  Nevertheless,  there 
are  occasions  in  which  pilasters  may  be  employed 
with  gi-eat  propriety ;  and  some  where  they  are,  on 
various  accounts,  even  preferable  to  columns. 

If  we  go  back  to  the  origin  of  things,  and  consider 
pilasters,  cither  as  representing  the  ends  of  partition 
walls,  or  trunks  of  trees  reduced  to  the  diameter  of 
the  round  trunks  which  they  accompany,  but  left 
square  for  greater  strength,  the  reason  for  dimin- 
ishing them  will,  in  either  case,  be  strong  and  evi- 
dent. 

It  is  likewise  an  error  to  assert  that  pilasters  are 
never  necessary,  but  that  columns  will  at  all  times 
answer  the  same  end ;  for,  at  the  angles  of  all  build- 
ings, they  are  evidently  necessary,  both  for  solidity 
and  beauty,  because  the  angular  support,  having  a 
greater  weight  to  bear  than  any  of  the  rest,  ought  to 
be  so  much  the  sti-ongcr ;  so  that  its  diameter  must 
cither  be  increased,  or  its  plan  altered  from  a  circle 
to  a  square.  The  latter  of  which  is  certainly  the 
most  reasonable  expedient  on  several  accounts,  but 
chiefly  as  it  obviates  a  very  strildng  defect,  occa- 
sioned by  employing  columns  at  the  angles  of  a 
building;  which  is,  that  the  angle  of  the  entablature 
is  left  hanging  in  the  air  without  any  support — a 
sight  very  disagreeable  in  some  oblique  views,  and 
in  itself  very  unsolid. 


It  is  indeed  customary,  in  porches  and  other  de- 
tached compositions,  to  employ  columns  at  the  an- 
gles ;  and  it  is  judicious  so  to  do,  for,  of  two  defects, 
the  least  is  to  be  prcfeiTcd. 

Engaged  pilasters  are  employed  in  churches,  gal- 
leries, halls,  and  other  interior  decorations,  to  save 
room,  for,  as  they  seldom  project  beyond  the  solid  of 
the  walls  more  than  fifteen  minutes  of  their  diameter, 
they  do  not  occupy  near  so  much  space  as  engaged 
columns.  They  are  likewise  employed  in  exterior 
decorations  ;  sometimes  alone,  instead  of  columns, 
on  account  of  their  being  less  expensive ;  at  other 
times  they  accompany  columns,  being  placed  behind 
them  to  support  the  springing  of  the  architi'avcs ;  or 
on  the  same  line  with  them,  to  fortify  the  angles : 
they  may  lilcewise  be  employed  instead  of  columns, 
detached  to  form  peristyles  and  porticoes,  but  there  is 
no  instance  of  this,  that  I  remember,  in  all  the  re- 
mains of  antiquity ;  neither  has  any  modern  archi- 
tect, I  believe,  been  so  destitute  of  taste  as  to  put  it 
in  practice. 

When  pilasters  are  used  alone,  as  principal  in  the 
composition,  they  should  project  fifteen  minutes  of 
their  diameter  beyond  the  walls,  which  give  them  a 
sufficient  boldness,  and,  in  the  Corinthian  and  Com- 
posite orders,  is  likewise  most  regular,  because  the 
stems  of  the  volutes,  and  the  small  leaves  in  flank 
of  the  capital,  arc  then  cut  exactly  through  their  mid- 
dles. But  if  the  cornice  of  the  windows  should  be 
continued  in  the  inter-pUaster,  as  is  sometimes  usual, 
or  if  there  should  be  a  cornice  to  mark  the  separation 
between  the  principal  and  second  story,  or  large  im- 
posts of  arches,  the  projection  must,  in  such  cases, 
be  increased,  provided  it  is  not  otherwise  sufficient  to 
stop  the  most  prominent  parts  of  these  decorations ; 
it  being  very  disagreeable  to  see  several  of  the  upper- 
most mouldings  of  an  impost  or  cornice  cut  away 
perpendicularly,  in  order  to  make  room  for  the  pilas- 
ter, Avhile  the  cornice  or  impost  on  each  side  projects 
considerably  beyond  it.  Mutilations  are,  on  all  oc- 
casions, studiously  to  be  avoided,  as  being  destructive 
of  perfection,  and  strong  indications  cither  of  inatten- 
tion or  ignorance  in  the  composer. 

Where  pilasters  are  placed  behind  columns,  and 
very  near  them,  they  need  not  project  above  seven 
and  one  half  minutes  of  their  diameter,  or  even  less, 
excepting  there  should  be  imposts  or  continued  cor- 
nices in  the  inter-pilaster ;  in  which  case,  what  has 
been  said  above  must  be  attended  to.     But  if  they 


PILASTERS. 


89 


be  far  behind  the  columns,  as  in  porticoes,  porches, 
and  peristyles,  they  should  project  ten  minutes  of 
their  diameter  at  least ;  and  when  they  are  on  a  line 
with  the  columns,  their  projection  is  to  be  regulated 
by  that  of  the  columns ;  and,  consequently,  it  can 
never  be  less  than  a  semi-diameter,  even  when  the 
columns  are  engaged  as  much  as  possible.  This 
extraordinary  projection,  however,  will  occasion  no 
very  great  deformity,  as  the  largest  apparent  breadth 
of  the  pilaster  will  exceed  the  least  only  in  the  ratio 
of  eleven  to  ten,  or  thereabouts.  But  if  columns  be 
detached,  the  angular  pilasters  should  always  be 
coupled  with  a  column,  to  hide  its  inner  flank ;  be- 
cause the  pilasters  will  otherwise  appear  dispropor- 
tionate when  seen  from  the  point  of  view  proper  for 
the  whole  building,  especially  if  the  fabric  be  small 
and  the  point  of  view  near. 

It  is  sometimes  customary  to  execute  pilasters 
without  any  diminution.  In  the  antiques  there  are 
several  instances  thereof,  as  well  as  of  the  contrary 
practice ;  and  Palladio,  Vignola,  Inigo  Jones,  and 
many  of  the  greatest  architects  have  frequently  done 
so.  Nevertheless,  it  is  certain  that  diminished  pilas- 
ters are,  on  many  accounts,  nmch  preferable.  There 
is  more  variety  in  their  form  ;  their  capitals  are  better 
proportioned,  both  in  the  whole  and  in  their  parts, 
particularly  in  the  Composite  and  Corinthian  orders ; 
and  the  irregularities  occasioned  by  the  passage  of 
the  architraves,  from  diminished  columns  to  undimin- 
ished pilasters,  are  thereby  avoided,  as  are  likewise 
the  difficulties  of  regularly  distributing  the  modil- 
lions  and  other  parts  of  the  entablature,  either  when 
the  pilasters  are  alone  or  accompanied  with  columns. 

Another  disagreeable  effect  of  undiminished  pilas- 
ters is  likewise  obviated  by  rejecting  them.  Indeed, 
I  am  at  a  loss  to  account  for  it,  and  it  is  diametri- 
cally opposite  to  a  received  law  in  optics.  I  im- 
agined it  might  be  the  result  of  some  defect  in  my 
own  sight,  till,  by  inquiry,  I  found  others  were  af- 
fected in  the  same  manner.  It  is  this  —  the  top  of 
the  shaft  always  appears  broader  than  the  bottom. 

The  shafts  of  pilasters  are  sometimes  adorned 
with  flutings  in  the  same  manner  as  those  of  col- 
umns, the  plan  of  which  may  be  a  trifle  above  a 
semicircle ;  and  they  must  be  to  the  number  of 
seven  on  each  face,  which  makes  them  nearly  of  the 
same  size  with  those  of  the  columns.  The  interval 
between  them  must  be  either  one  third  or  one  fourth 
of  the  flute  in  breadth ;  and  when  the  pilaster  is 
12 


placed  on  the  pavement,  or  liable  to  be  broken  by 
the  touch  of  passengers,  the  angle  may  be  rounded 
off",  in  the  form  of  an  astragal ;  between  which  and 
the  adjoining  flute  there  must  be  a  fillet  or  interval 
of  the  same  size  with  the  rest,  as  in  the  porch  of  the 
Pantheon,  at  Rome. 

The  flutes  may,  like  those  of  columns,  be  filled 
with  cablings  to  one  thurd  of  their  height,  either  plain, 
and  shaped  like  an  astragal,  or  enriched,  according  as 
the  rest  of  the  composition  is  simple  or  much  adorned. 
Scamozzi  is  of  opinion  that  there  should  be  no  flut- 
ings on  the  sides  of  engaged  pilasters,  but  only  in 
front;  and,  whenever  cornices  or  imposts  are  con- 
tinued home  to  the  pilaster,  this  should  be  partic- 
ularly attended  to,  that  the  different  mouldings  of 
these  members,  by  entering  into  the  cavities  of  the 
flutes,  may  not  be  cut  off"  in  irregular  and  disagreea- 
ble forms.  But  if  the  flanks  of  the  pilasters  are  en- 
tirely free,  it  may  be  as  well  to  emich  them  in  the 
same  manner  as  the  front,  provided  the  flutes  can  be 
so  distributed  as  to  have  a  fillet  or  interval  adjoining 
to  the  wall  —  which  is  always  necessary  to  mark  the 
true  shape  of  the  pilasters  distinctly. 

The  capitals  of  Tuscan  or  Doric  pilasters  are  pro- 
filed in  the  same  manner  as  those  of  the  respective 
columns;  but  in  the  capitals  of  the  other  orders, 
there  are  some  trifling  differences  to  be  observed.  In 
the  antique  Ionic  capital,  the  extraordinary  projection 
of  the  ovolo  makes  it  necessary  either  to  bend  it  in- 
wards considerably  towards  the  extremities,  that  it 
may  pass  behind  the  volutes,  or  instead  of  keeping 
the  volutes  flat  in  front,  as  they  commonly  are  in  the 
antique,  to  twist  them  outwards,  till  they  give  room 
for  the  passage  of  the  ovolo.  Le  Clerc  thinks  the 
latter  of  these  expedients  the  best ;  and,  that  the  arti- 
fice may  not  be  too  striking,  the  projection  of  the 
ovolo  may  be  considerably  diminished,  as  in  plate  56, 
Fig.  2 ;  which,  as  the  moulding  can  be  seen  in  front 
only,  will  occasion  no  disagreeable  effect. 

The  employing  half  or  other  parts  of  pilasters  that 
meet,  and,  as  it  were,  penetrate  each  other's  inward 
or  outward  angles,  should,  as  much  as  possible,  be 
avoided,  because  it  generally  occasions  several  irreg- 
ularities in  the  entablatures,  and  sometimes  in  the 
capital  also.  Particular  care  must  be  taken  never  to 
introduce  more  than  one  of  these  breaks  in  the  same 
place,  for  more  can  never  be  necessary.  In  many  of 
the  churches  at  Rome  we  see  half  a  dozen  of  them 
together,  which  produce  a   long  series  of  undulated 


90 


ARCADES  AND  ARCH  E  S.  — PEDESTALS. 


capitals  and  bases,  and  a  number  of  mutilated  parts 
in  the  entablature,  than  which  nothing  can  be  more 
confused  or  disagreeable. 


ARCADES    AND    ARCHES. 

The  arch  is,  without  doubt,  a  Roman  invention ;  * 
and  from  this  circumstance  the  oldest,  which  is  the 
semicircular,  is  called  the  Roman  arch.  The  time  of 
its  introduction  may  be  looked  upon  as  a  new  epoch 
in  the  science  of  architecture,  for  by  this  change  the 
Romans  succeeded  in  laying  the  foundation  for  a 
complete  revolution  of  taste  and  conception.  Says 
Gwilt,  in  his  Encyloptedia  of  Architecture,  "  This 
change,  by  various  steps,  led  through  the  basilica  to 
the  construction  of  the  extraordinary  Gothic  cathe- 
drals of  Europe,  in  its  progress  opening  beauties  in 
the  art  of  which  the  Greeks  had  not  the  remotest 
conception."  The  principal  feature  of  the  Roman 
architecture  is  the  use  of  the  arch  and  circle,  each 
moulding  being  composed  of  some  portion;  while 
those  of  the  Grecian  are  composed  entirely  of  sec- 
tions of  the  cone.  An  arcade  is  a  series  of  arches, 
separated  by  one  or  more  columns,  with  their  imposts 
and  piers,  and  is  often  one  of  the  most  pleasing,  as 
well  as  imposing,  objects  which  architecture  affords ; 

*  We  are  aware  that,  -n-ere  we  to  pass  oyer  this  point  without  al- 
luding to  the  discovery  of  an  arch  at  Thebes,  we  should  not  feel 
warranted  in  making  the  above  assertion.  An  account  of  this  arch 
may  be  found  in  "Wilkinson's  Customs  of  the  Ancient  Egyptians, 
vol.  iii.  pp.  221  and  263.  To  the  arch  of  Thebes  Mr.  W.  assigns 
the  date  of  1500  B.  C.  But  as  this  structure,  if  one  may  judge  from 
his  delineation,  is  so  purely  Roman  in  its  character,  its  antiquity  is 
doubted  by  most  authors.  The  arch  in  the  tomb  of  Saccara  is  the 
other  to  which  he  alluded,  and  is  from  his  delineation  simply  a  lining, 
and  is  not  capable  of  sustainmg  any  weight,  which  is  the  office  of 
the  arch.  Mr.  Wilkinson  assigns  as  a  reason  for  the  Egyptians  not 
using  the  mode  of  construction  requiring  the  arch,  that  there  would 
be  difficulty  attending  the  repairing  of  any  accident  that  might  befall 
it.  In  regard  to  this  argument,  it  would  seem,  at  any  rate,  that,  to 
an  engineer  who  could  erect  the  Pyramid  of  Cheops,  some  way 
would  suggest  itself  for  the  repairs  of  a  simple  arch,  had  he  ever 
conceived  of  its  construction.  lie  again  speaks  of  the  consequences 
attending  the  decay  of  a  single  block,  &c.  In  regard  to  this  it  is 
argued,  that,  in  the  case  alluded  to,  the  balance  on  the  outer  side  or 
back  of  each  course  would  preserve  the  opening  in  some  form  with- 
out any  arch  at  all.  And  besides  this,  when  we  take  into  considera- 
tion the  fact  that  so  much  time  and  labor  was  expended  to  procure 
the  immense  stones  for  architraves,  which  could  have  been  avoided 
in  many  instances  by  the  use  of  the  arch,  it  seems  that,  had  it  ex- 
isted in  their  very  midst,  some,  to  say  the  least,  would  have  ven- 
tured to  use  it-  —  Editohs. 


and  the  utility  of  them  in  some  climates,  for  shelter 
from  rain  and  heat,  is  obvious.  We  have  given,  in 
plate  40,  designs  for  arcades  with  and  without  pedes- 
tals. The  proportions  are  very  nearly  the  same  as 
given  by  Chambers ;  and,  as  will  be  seen  by  exami- 
nation, they  are  different  in  each  of  the  orders.  We 
should  have  been  pleased  to  have  given  examples  of 
arcades  above  arcades ;  but  our  limits  would  not  allow 
it.  We  will  state  here,  however,  that  as  in  orders 
above  orders  the  Tuscan  invariably  stands  at  the  bot- 
tom, and  above  it  the  Doric  ;  immediately  above  tlus 
the  Ionic,  and  next  the  Corinthian  ;  and,  should  the 
Composite  be  used,  its  place  is  above  the  Corinthian. 
The  lower  diameter  of  the  shaft  immediately  above 
the  base  of  each  column  is  of  the  size  of  the  one 
next  below  it  at  the  top  just  below  the  capital ;  these 
dimensions  will,  of  course,  govern  the  proportions  of 
the  entire  order.  If  the  balustrade  be  used  in  the 
openings,  it  should  extend  from  pier  to  pier  at  the 
side  of  the  column,  and  its  whole  height  should  be 
the  top  of  the  pedestal,  the  height  of  the  baluster,  or 
its  dimension,  is  the  die  of  the  pedestal.  The  rails 
above  and  below  them  are  a  continuation  of  its  cor- 
nice and  base.  The  use  of  arcades  above  arcades 
is  pretty  generally  confined  to  public  buildings,  as, 
among  the  Romans,  to  their  theatres  and  amphithea- 
tres ;  they  have,  however,  been  much  employed  in 
Europe ;  and  in  the  magnificent  design  made  by  Inigo 
Jones,  for  the  palace  at  Whitehall,  are  to  be  found 
some  very  fine  examples.  —  Editors, 


PEDESTALS. 

Most  writers  consider  the  pedestal  as  a  necessary  part  of  the  order, 
without  which  it  is  not  esteemed  complete.  It  is,  indeed,  a  matter 
of  small  importance  whether  it  be  considered  in  that  light  or  as  a 
distinct  composition.  Vitruvius  only  mentions  it  as  a  necessar)-  part 
in  the  construction  of  a  temple,  without  signifying  that  it  belongs  to 
the  order,  or  assigning  any  particular  proportions  for  it,  as  ho  does 
for  the  parts  of  the  column  and  the  entablature.  But  triangular, 
circular,  or  polygonal  pedestaLs,  or  such  as  are  swelled  and  have 
their  die  in  the  form  of  a  baluster,  or  are  surrounded  with  cinctures, 
are,  in  no  case,  to  be  made  use  of  in  buildings.  Such  extravagances, 
though  frequent  in  some  foreign  countries,  are  now  laid  aside  wher- 
ever good  taste  prevails. 


A  pedestal,  like  a  column  or  an  entablature,  is  com- 
posed of  three  principal  parts,  which  are  the  base,  the 
body  or  the  die,  and  the  cornice.     The  die  is  always 


ri  III 


# 


% 

A 


1 


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!       -.- 


VI'}.: 


L_ 


-—  '/i-^r  -  4 


PEDESTALS. 


91 


nearly  of  the  same  figure,  being  constantly  either  a 
cube  or  a  parallclopiped  ;  but  the  base  and  cornice 
are  varied,  and  adorned  with  more  or  less  mouldings, 
according  to  the  simplicity  or  richness  of  the  compo- 
sition in  which  the  pedestal  is  employed.  Hence 
pedestals  are,  like  columns,  distinguished  by  the 
names  of  Tuscan,  Doric,  Ionic,  Corinthian,  and  Com- 
posite. 

Some  authors  are  very  averse  to  pedestals,  and 
compare  a  column  raised  on  a  pedestal  to  a  man 
mounted  on  stilts,  imagining  that  they  were  first  in- 
troduced merely  through  necessity  and  for  want  of 
columns  of  a  sufficient  length. 

It  does  not  seem  proper  to  suppose  that  they  were 
first  introduced  merely  through  want  of  columns  of 
a  sufficient  length,  since  there  are  many  occasions  on 
which  they  are  evidently  necessary,  and  some  in 
which  the  order,  were  it  not  so  raised,  would  lose 
much  of  its  beautiful  appearance.  Thus,  within  our 
churches,  if  the  columns  supporting  the  vault  were 
placed  immediately  on  the  ground,  the  seats  would 
hide  their  bases  and  a  good  part  of  the  shafts  ;  and 
in  the  theatres  of  the  ancients,  if  the  columns  of  the 
scene  had  been  placed  immediately  on  the  stage,  the 
actors  would  have  hid  a  considerable  part  of  them 
from  the  audience ;  for  which  reason  it  was  usual  to 
raise  them  on  very  high  pedestals,  as  was  likewise 
customary  in  their  triumphal  arches  ;  and  in  most  of 
their  temples  the  columns  were  placed  on  a  basement 
or  continued  pedestal,  so  that  the  whole  order  might 
be  exposed  to  view,  notwithstanding  the  crowds  of 
people  with  which  these  places  were  frequently  sur- 
rounded. And  the  same  reason  wiU  authorize  the 
same  practice  in  our  churches,  theatres,  courts  of  jus- 
tice, and  other  public  buildings  where  crowds  fre- 
quently assemble.  And  in  a  second  order  of  arcades 
there  is  no  avoiding  pedestals,  as  without  them  it  is 
impossible  to  give  the  arches  any  tolerable  proportion. 
These  instances  will  sufficiently  show  the  necessity 
of  admitting  pedestals  in  decorations  of  architecture. 
With  regard  to  the  proportion  which  their  height 
ought  to  bear  to  that  of  the  columns  they  are  to  sup- 
port, it  is  by  no  means  fixed  —  the  ancients  and  mod- 
erns, too,  having  in  their  own  works  varied  greatly 
in  this  respect,  and  adapted  their  proportions  to  the 
occasion,  or  to  the  respective  purposes  for  which  the 
pedestals  were  intended.  Thus,  in  the  amphitheatres 
of  the  ancients,  the  pedestals  in  the  superior  orders 
were  generally  low,  because  in  the  apertures  of  the 


arches  they  served  as  rails  to  enclose  the  portico,  and 
therefore  were,  for  the  conveniency  of  leaning  over, 
made  no  higher  than  was  necessary  to  prevent  acci- 
dents ;  and  the  case  is  the  same  in  most  of  our  mod- 
ern houses,  where  the  height  of  the  pedestals  in  the 
superior  orders  is  generally  determined  by  the  sills  of 
the  windows.  The  ancients,  in  their  theatres,  made 
the  pedestals  in  the  first  order  of  their  scene  high,  for 
the  reason  mentioned  in  the  beginning  of  this  chap- 
ter ;  but  the  pedestals  in  the  superior  orders  were  very 
low,  their  chief  use  being  to  raise  the  columns  so  as 
to  prevent  any  part  of  them  from  being  hid  by  the 
projection  of  the  cornice  below  them  ;  and  thus,  on 
different  occasions,  they  used  different  proportions, 
being  chiefly  guided  by  necessity  in  their  choice. 

Nevertheless,  writers  on  architecture  have  always 
thought  it  incumbent  upon  them  to  fix  a  certain  de- 
terminate proportion  for  the  pedestal,  as  well  as  for 
the  parts  of  the  order.  It  would  be  useless  to  enu- 
merate in  this  place  their  different  opinions ;  but  I 
must  beg  leave  to  observe  that  Vignola's  method  is 
the  only  true  one.  His  pedestals  are  all  in  the  orders 
of  the  same  height,  being  one  third  of  the  column ; 
and  as  their  bulk  increases  or  diminishes,  of  course 
in  the  same  degree  as  the  diameters  of  their  respec- 
tive columns  do,  the  character  of  the  order  is  always 
preserved,  which,  according  to  any  other  method,  is 
impossible. 

With  regard  to  the  divisions  of  the  pedestals,  if 
the  whole  height  be  divided  into  nine  parts,  one  of 
them  may  be  given  to  the  height  of  the  cornice,  two 
to  the  base,  and  the  remaining  six  to  the  die ;  or  if 
the  pedestal  is  lower  than  ordinary,  its  height  may 
be  divided  into  eight  parts  only,  of  which  one  may 
be  given  to  the  cornice,  two  to  the  base,  and  five  to 
the  die,  as  Palladio  has  done  in  his  Corinthian  order, 
and  Perault  in  aU  the  orders.* 

The  plan  of  the  die  is  always  made  equal  to  that 
of  the  plinth  of  the  column ;  the  projection  of  the 
cornice  may  be  equal  to  its  height ;  and  the  base, 
being  divided  into  three  parts,  two  of  them  will  be 
for  the  height  of  the  plinth,  and  one  for  the  mould- 
ings, of  which  the  projection  must  be  somewhat  less 
than  the  projection  of  the  cornice,  so  that  the  whole 
base  may  be  covered  and  sheltered  by  it. 

These  measures  are  common  to  aU  pedestals ;  and 
in  plate  41  there  are  proper  designs  for  the  Tuscan, 


Ordonnance  dcs  cinq  Especes  de  Colonnes,  1  Partie,  ch.  6  et  7. 


92 


IMPOSTS. 


Doric,  Ionic,  and  Corinthian  orders,  in  which  the 
forms  and  dimensions  of  the  minuter  parts  are 
acciuately  drawn  and  figured.  With  regard  to  the 
application  of  pedestals,  it  must  be  observed  that 
when  columns  are  entirely  detached,  and  at  a  consid- 
erable distance  from  the  wall,  as  when  they  are  em- 
ployed to  form  porches,  peristyles,  or  porticoes,  they 
should  never  be  placed  on  detached  pedestals,  for 
then  they  may  indeed  be  compared  to  men  mounted 
on  stilts,  as  they  have  a  very  weak  and  tottering 
appearance. 

The  base  and  cornice  of  these  pedestals  must  run 
in  a  straight  line  on  the  outside  throughout;  but  the 
dies  arc  made  no  broader  than  the  plinths  of  the 
columns,  the  interv'als  between  them  being  filled 
with  balusters,  which  is  both  really  and  apparently 
lighter  than  if  the  whole  pedestal  were  a  continued 
solid. 

TABLE, 

Showing  the  Height  of  Pedestals  in  antique  and 
modem  Works  in  Minutes,  each  one  sixtieth  of 
the  Diameter  of  the  Shaft, 


Doric,  . 


lowic, 


CoMPOSlTS, 


{Palladio, 
Scamozzi 

!  Temple  of  Fortuna  Virilis, 
Coliseum, 
Palladio, 
Scamozzi, 

IArcb  of  Constantine, ... 
Coliseum, 
Palladio 
Scamozzi , ■ 

Arch  of  Titus 

Arch  of  the  Goldsmiths, 

Palladia 

Scamozzi, 

Arch  of  Sep.  Severus,  . . 


26 

30 

44 

33J 

28§ 

30 

lli 

23 

23J 

30 

55 

46 

33 

30 

30 


Mouldings 
above 
Plinth. 


14 
15 

19f 

9^ 
14* 
15 
29 

11* 

14* 

15 

30 

25i 

17 

15 

30| 


80 

68f 
93f 

97J 

82i 
153" 

78 

93 
132J 
141 
144^ 
133 
112J- 
140^ 


20 

22| 

23^ 

17 

2U 

22^ 

29^ 

19^ 

19 

22^ 

29 

25^ 

17 

221 

29| 


Total 
Height 


140 

136Jj 

180f 

14U 

162J. 

150 

228 

131f 

150 

200 

255 

241 

200 

180 

182^ 


On  plate  41  will  be  found  designs  for  pedestals  of 
the  different  orders.  They  are  figured  by  the  same 
scale  with  which  the  order  should  be  drawn  in  which 
they  may  be  employed. 

Fig.  2.  In  this  figure  is  shown  the  manner  of 
striking  or  working  a  raking  moulding  to  fit  and 
mitre  with  the  same  on  a  horizontal  line  or  flank. 
First  divide  the  width  of  the  moulding  into  1,  2,  3, 


and  4  parts,  as  in  A ;  raise  a  perpendicular  line  in 
B,  at  O ;  trace  the  cur^'e  of  the  moulding  from  the 
intersection  of  1,  2,  3,  4,  on  the  curve  line  of  the 
moulding ;  draw  a,  b,  c,  d,  e,  f,  g,  h,  at  right  angles 
with  the  perpendicular  line  O,  to  the  points  /;,/,  d,  b, 
in  the  curve  or  face  of  the  moulding ;  transfer  to  A. 
a  b,  c  d,  ef,  g  h.  In  the  like  manner,  the  curve  at  C 
may  be  found.  All  to  mitre  in  their  several  parts 
with  each  other. 


IMPOSTS. 

Imposts  are  explained  in  the  glossary.  By  some,  however,  they 
are  called  the  walls  back  of  the  inserted  column,  rising  from  the 
base  to  the  spring  line  of  the  arch,  and  extending  on  each  side  of 
the  column  about  thirty  minutes  —  forming  the  side  of  the  apertures 
of  doors  or  mndows,  and,  when  used  without  the  columns,  are 
appropriately  termed  pilasters.  But  they  are  most  generally  used 
for  those  assemblages  of  moulding  which  divide  the  perpendicular 
part  of  the  wall  from  the  spring  line  of  the  arch.  In  some  in- 
stances regular  pilasters  are  introduced,  when  the  colimin  may  be 
termed  isolated,  as  it  stands  detached  from  the  walls.  We  find 
imposts  introduced  in  the  Temple  of  Solomon  ;  and  they  are  com- 
mon in  Koman  edifices  ;  as  in  the  Arch  of  Titus,  and  most  of  theii 
other  triumphant  arches,  &c.  In  most  parts  of  Europe  imposts  are 
found,  as  also  in  some  parts  of  the  United  States.  The  origin  of  this 
style  of  building  cannot  be  clearly  traced.  However  elegant  its 
aspect  in  many  instances  may  be,  it  seems  now  to  be  giving  place  to 
a  more  magnificent  and  majestic  style  of  architecture.  Where  we 
once  saw  one  range  of  columns  rising  above  another,  each  support- 
ing a  distinct  entablature,  we  now  find  the  whole  height  supplied 
by  one  length,  thus  preserving  the  principles  of  good  taste. 


An  impost  is  the  capital  of  a  pier  or  pilaster  which 
receives  the  arch  in  the  arcades  of  the  Roman  order. 
On  plate  42  we  have  given  designs  for  the  different 
orders,  and  have  figured  them  to  be  drawn  by  the 
same  scale  of  minutes  with  which  the  order  is  drawn 
to  which  they  may  be  applied.  No.  4  is  from  a  de- 
sign by  Vignola ;  the  rest  are  by  Sir  William  Cham- 
bers. 

Bases.  —  No.  1  is  the  Tuscan  base ;  No.  2  is  the 
Doric;  and  No.  3  is  the  Attic.  The  last  named 
Chambers  has  used  with  all  his  orders,  excepting 
the  Tuscan.  This  base  was  used  by  the  ancients 
to  a  great  extent;  and  they  have  not,  to  say  the 
least,  in  many  instances  made  any  improvement 
—  Editors. 


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BALUSTRADES. 


98 


BALUSTRADES. 

The  baluster  is  not  found  in  the  works  of  the  an- 
cients, but  owes  its  origin  to  the  restoration  of  the 
art  in  Italy.  It,  like  the  column,  consists  of  the  cap- 
ital, shaft,  and  base.  The  most  ancient  examples 
were  of  the  shape  of  a  stunted  column,  and  not  un- 
frequently  were  crowned  with  a  disproportioned  Ionic 
capital.  Many  forms  have  been  given  to  them  by 
the  later  masters,  and  we  may  safely  say  that  the 
invention  is  one  of  the  most  useful  as  well  as  orna- 
mental that  was  produced  by  the  Italians.  A  balus- 
trade is  a  series  of  balusters  standing  upon  a  base, 
and  croAvned  with  a  capital  or  rail,  —  this  capital 
and  base  being  of  the  same  outline  in  its  detail  as 
those  of  the  pedestal  which  accompany  them.  It  is 
proposed  by  Blondel  that  balusters  and  balustrades 
should  partake  of  the  character  of  the  edifice  they 
are  to  be  employed  upon ;  and  by  some  their  species 
has  been  so  arranged  as  to  appropriate  a  design  to 
each  order,  and  in  the  works  of  such  they  are  known 
by  the  name  of  Tuscan,  &c.  The  general  riUes  to 
be  observed  in  the  construction  of  balustrades  are, 
that  the  balusters  be  of  an  odd  number,  and  the  dis- 
tance between  them  equal  to  half  their  larger  diam- 
eter, which  will  produce  an  equality  between  the 
open  and  solid  spaces ;  and  a  half  baluster  should 
always  be  placed  against  the  pedestal.  When  the 
balustrade  is  formed  without  pedestals,  as  is  often 
the  case  where  balusters  are  placed  between  columns, 
the  half  baluster  may  be  omitted.  The  pedestals  of 
balustrades  should  always  be  placed  directly  over  the 
column,  and  the  die  be  of  the  same  width  as  the  di- 
ameter of  the  column  at  the  top.  Where  the  columns 
stand  together  as  in  what  is  termed  coupled  columns, 
as  seen  at  A,  in  plate  43,  the  pedestal  should  extend 
over  both  entire.  Also,  where  a  balustrade  terminates 
against  a  roof  or  pediment,  the  termination  should 
be  by  a  pedestal,  and  it  should  commence  where  the 
balustrade  begins  to  diminish,  be  the  distance  more 
or  less ;  and  in  no  case  should  the  baluster  be  cut  to 
the  roof.  The  pedestals,  as  before  stated,  should 
stand  directly  over  the  columns,  —  the  distances  be- 
tAveen  them  would,  of  course,  depend  upon  the  in- 
tercolumniation,  —  but  where  no  columns  are  used, 
either  seven  or  nine  whole  balusters,  with  the  half  ones, 


have  been  recommended  as  producing  the  best  efiect ; 
for  when  the  pedestals  stand  too  near  each  other, 
they  present  a  heavy  and  clumsy  appearance  to  the 
work  ;  and  where  they  are  too  far  apart,  the  work  will 
appear  weak.  The  bulbs  or  bellies  of  balusters  are 
often  enriched ;  which,  for  stairs  and  highly-finished 
interiors,  is  quite  requisite.  In  regard  to  the  heights 
of  balustrades,  when  they  are  used  as  a  protection  to 
terraces,  or  before  windows,  they  should  be  not  less 
than  two  feet  six  inches,  nor  more  than  three  feet 
high  ;  but  when  they  are  used  as  merely  ornamental 
appendages  to  a  building,  they  should  be,  according 
to  the  majority  of  authors,  not  more  than  two 
thirds  of  the  height  of  the  entablature  over  which 
they  stand,  nor  less  than  two  thirds,  without  count- 
ing the  plinth,  the  height  of  which  must  be  sufii- 
cient  to  leave  the  entire  baluster  exposed  to  view 
from  the  best  point  of  sight  for  viewing  the  building. 
Palladio  has,  however,  in  some  instances,  made  the 
balustrade  the  height  of  the  entire  entablature,  as  at 
the  Valmarana  Palace.  Inigo  Jones  has,  in  some 
instances,  followed  his  example ;  but  this  was  not  the 
usual  practice  of  either.  We  have  before  stated, 
that  the  moderns  have  given  to  the  baluster  a  variety 
of  shapes.  On  plate  43  we  have  given  the  designs 
recommended  by  Chambers,  with  the  method  of  pro* 
portioning  them,  in  the  manner  adopted  by  him. 
No.  1  is  the  Tuscan ;  No.  2  the  Doric  and  Ionic ; 
No.  3  the  Corinthian  and  Composite.  No.  4  is  a 
design  for  a  Tuscan  baluster,  and  has  generally  been 
executed  square.  Nos.  5,  6,  and  7  are  designs  for 
double-bellied  balusters,  and  are  intended  principally 
for  balconies  and  terraces,  the  rail  and  pedestal  being 
the  same  height  as  in  other  designs.  Chambers  has 
designated  them  respectively  the  Tuscan,  Doric,  and 
Ionic  and  Corinthian.  The  method  of  proportioning 
them  to  the  order  is  as  follows :  After  ascertaining 
the  height,  as  before  directed,  divide  it  into  thirteen 
parts ;  of  which,  give  two  to  the  rail,  eight  to  the 
baluster,  and  the  remaining  three  to  the  base  :  if  the 
baluster  is  required  to  be  less,  divide  the  height  into 
fourteen  parts,  giving  two  to  the  rail,  eight  to  the 
baluster,  and  four  to  the  base.  One  of  these  parts 
is  a  module  for  determining  the  rest,  and  is  divided 
into  nine  other  parts,  called  minutes.  From  what 
has  been  said,  the  whole  on  plate  43  will,  without 
doubt,  be  clearly  understood.  —  Editors. 


94: 


GRECIAN    ORDERS. 


GRECIAN    ORDERS. 

The  Doric,  the  Ionic,  and  the  Corinthian  were  the  only  orders  of 
architecture  employed  by  the  Greeks.  The  Tuscan  and  Composite 
were  used  only  in  Italy  —  the  one  more  rude,  the  other  more  orna- 
mented, than  the  Greek  orders,  -which  occupied  a  middle  rank.  To 
attain,  therefore,  a  proper  knowledge  of  the  true  principles  of  archi- 
tecture, the  student  shoiJd  devote  most  of  his  attention  to  the  three 
Greek  orders ;  not  only  because  in  them  these  principles  arc  the 
most  displayed,  but  because  of  all  the  monuments  of  antiquity 
which  have  subsisted  to  modem  times  few,  or  perhaps  none,  can  be 
pointed  out  ra  which  the  Roman  or  Italic  mode  of  construction  is 
certainly  to  be  traced. 


DEFINITIONS. 

1.  If  any  number  of  frustums  of  cones,  or  frus- 
tums of  conoids  of  similar  solids  and  equal  magni- 
tudes with  each  other,  be  so  arranged  that  their 
bases,  which  are  the  thickest  ends  of  the  frustums, 
may  stand  upon  or  in  the  same  horizontal  plane, 
and  their  axes  in  the  same  plane  with  each  other 
and  perpendicular  to  the  horizon  ;  and  if  on  the  tops 
of  these  frustums  be  laid  a  continued  beam ;  and  if 
over  this  beam  be  laid  the  ends  of  a  number  of  equi- 
distant joists,  the  other  ends  being  either  supported  in 
the  same  manner,  or  by  a  wall  or  any  piece  of  build- 
ing whatever,  so  that  the  upper  and  under  surfaces 
may  be  in  the  same  horizontal  planes ;  and  if  over 
the  ends  of  these  beams  be  laid  another  beam  paral- 
lel to  the  former,  which  lays  upon  the  fr-ustums,  but 
projecting  farther  out  from  the  axis  of  the  columns 
than  the  vertical  face  of  the  lower  beam  which  is 
over  the  frustums  ;  and  if  this  beam  supports  the 
ends  of  rafters  whose  upper  surfaces  lay  in  the  same 
inclined  plane,  so  as  to  support  a  covering  or  roof,  — 
the  whole  of  this  mass,  together  with  the  frustums 
supporting  it,  is  called  an  order. 

2.  K  the  bottom  or  lower  end  of  the  frustum 
finish  with  an  assemblage  of  mouldings,  projecting 
equally  aU  round  beyond  the  bottom  of  the  frustum, 
then  this  assemblage  is  called  a  base. 

3.  If  the  upper  end  of  the  frustum  finish  with 
mouldings  or  any  kind  of  ornaments,  and  if  these 
ornaments  or  mouldings  be  covered  with  a  solid, 
whose  upper  end  and  lower  sides  are  square,  and  the 
vertical  or  perpendicular  sides  rectangles,  then  this 
solid,  together  with  the  ornaments  or  mouldings 
under  it,  is  called  a  capital. 


4.  If  the  frustum  has  no  base,  then  the  capital 
and  frustum  together  are  called  a  frustum  column ; 
but  if  the  frustum  has  a  base,  then  the  base,  frus- 
tum, and  capital,  taken  together,  are  simply  called  a 
column. 

5.  The  mass  supported  by  the  columns  is  called 
an  entablature. 

6.  The  under  beam  of  the  entablature  is  called  an 
architrave  or  epistylium. 

I.  The  space  comprehended  bet^veen  the  upper 
side  of  the  epistylium  or  architrave  and  the  under 
edge  of  the  beam  over  the  joists,  is  called  the  frieze 
or  zophorus. 

8.  The  edge  or  profile  of  the  inclined  roof  sup- 
ported by  the  joists  or  cross  beams,  jetting  out  be- 
yond the  face  of  the  zophorus  or  frieze,  is  called  a 
cornice. 

9.  The  lowest  or  thickest  part  of  a  column  is 
called  the  diameter  of  the  coluinn. 

10.  Half  of  the  diameter  of  the  column  is  called 
a  module. 

II.  If  a  module  be  divided  into  thirty,  or  any 
other  number  of  equal  parts,  then  these  parts  are 
called  minutes. 

12.  The  shortest  distance  from  the  bottom  of  the 
frustum  of  one  column  to  the  bottom  of  the  frus- 
tum of  the  next  column  is  called  the  intercolumni- 
ation. 

13.  When  the  ijitercolumniation  is  one  diameter 
and  half  a  column,  it  is  called  pijcnostyle,  or  col- 
timns  thick  set. 

14.  When  the  intercolumniation  has  two  diam- 
eters of  the  columns,  then  it  is  called  si/style. 

15.  When  the  space  bct^-een  the  columns  is  two 
diameters  and  a  quarter,  then  the  intercolumniation 
is  called  evstyle. 

16.  When  the  intercolumniation  is  three  diam- 
eters of  the  columns,  then  it  is  called  decastyle. 

17.  When  the  distance  betw'een  the  columns  has 
four  diameters  of  the  columns,  then  that  intercolum- 
niation is  called  arccostyle,  or  columns  thin  set. 

18.  When  there  are  four  columns  in  one  row,  then 
that  number  is  called  tetrastyle. 

19.  When  there  are  six  columns  in  ojic  row,  then 
it  is  called  hexastyle. 

20.  Wlicn  there  are  eight  columns  in  one  row, 
then  it  is  called  octastyle. 


GRECIAN    DORIC. 


95 


GRECIAN    DORIC. 

The  first  Grecian  order  in  point  of  antiquity  is  the  Doric,  so 
called  from  the  Dores,  a  small  tribe  in  Greece ;  or,  as  some  say, 
from  Dorus,  an  Achaian  chief,  who  first  employed  the  order  in 
erecting  a  temple  to  Juno,  at  Argos. 


DEFINITIONS. 

1.  If  through  the  axis  of  the  shaft  be  supposed  to 
pass  twenty  vertical  planes,  making  equal  angles 
with  each  other,  which  wiU  cut  the  surface  of  the 
column  in  twenty  places ;  and  if  the  surface  of  the 
column  be  curved  or  hoUowcd  between  each  two 
lines,  from  the  bottom  to  the  top  of  the  shaft,  ter- 
minating immediately  under  the  lowest  annulet, — 
then  the  shaft  will  have  twenty  curved  sides,  and  as 
many  angles  ;  and  if  nearly  at  the  upper  end  of  the 
shaft  be  cut  one  or  more  grooves,  of  an  equal  depth 
from  the  surface  of  the  hollowing,  each  groove  being 
parallel  to  the  annulets  under  the  echinus,  then  a 
column  so  formed  is  called  Doric. 

2.  That  part  of  the  column  contained  between  the 
upper  channel  and  the  lower  annulets  is  called  the 
hypotrachelion,  neck,  or  frieze  of  the  capital. 

3.  That  part  of  the  Doric  column  comprehending 
the  abacus,  echinus,  annulets,  and  hypotrachelion,  is 
called  a  Doric  capital. 

4.  If  the  ends  of  the  cross  beams  in  the  frieze 
which  lay  upon  the  architrave  be  at  right  angles 
to  the  sides  of  the  beams,  and  parallel  to  the  front 
or  the  architrave ;  and  if  the  two  vertical  right  angles 
of  each  beam  formed  by  the  two  vertical  sides  and 
the  ends  be  cut  away  by  vertical  planes,  making 
equal  angles  wath  the  sides  and  ends,  —  that  is,  135 
degrees  with  each,  —  and  if  two  other  vertical  chan- 
nels are  cut  on  the  end,  so  that  the  planes,  which  are 
three  in  number,  left  on  the  ends  of  each  beam,  may 
be  equal  rectangles,  and  the  two  sides  of  each  chan- 
nel make  135  degrees  with  the  ends  of  the  joists, 
and  are  so  disposed  that  there  may  be  a  rectangle 
next  to  each  semi-channel,  and  then  two  whole 
channels,  leaving  a  rectangle  in  the  middle,  —  the  end 
of  the  beam  so  formed  is  called  a  trigli/pk. 

5.  K  the  spaces  between  the  triglyph  be  filled  up 
with  planes  parallel  to  the  front  of  the  triglyphs  or 
to  the  front  of  the  architrave ;  and  if  these  planes 
be  in  the  same  plane  with  each  other  and  recessed 


beyond  the  ends  of  the  triglypn,  so  as  to  show  a 
small  part  of  the  vertical  sides  of  the  beams,  —  that  is, 
to  be  farther  in  than  the  channels  of  the  triglyph,  — 
then  these  spaces  so  filled  up  are  called  metopes. 

6.  If  the  front  of  the  beam  which  supports  the 
rafters  that  lay  upon  the  joists  projects  at  some  dis- 
tance beyond  the  face  of  the  triglyph,  the  plane  of 
the  front  being  parallel  to  the  ends  of  the  beam ; 
and  if  a  recess  be  cut  from  this  beam  directly  over 
the  metopes,  the  plane  of  the  front  of  the  recess 
being  parallel  to,  and  having  a  small  projecture  over, 
the  metopes,  and  the  ends  of  the  recesses  over  the 
metopes  be  in  the  same  plane  with  the  vertical  sides 
of  the  beam,  —  then  that  part  of  the  front  of  the 
beam  over  the  triglyph  is  called  the  capital  of  the 
triglyph. 

7.  The  whole  face  of  the  work  comprehended 
between  the  upper  edge  of  the  beam  which  forms 
the  capital  of  the  triglyphs,  and  the  lower  end  of  the 
triglyphs  and  metopes,  is  called  a  Doric  frieze. 

8.  If  from  the  top  of  the  architrave  project  a 
fillet  whose  upper  edge  is  in  the  same  plane  with  the 
top  of  the  architrave  or  the  lower  end  of  the  trigljrph, 
the  front  of  the  fillet  being  a  vertical  plane  parallel 
to  the  front  of  tlie  architrave,  having  a  small  projec- 
ture beyond  the  front  of  the  triglyph,  this  fillet  being 
supposed  to  be  continued  the  whole  length  of  the 
architrave,  and  returning  in  the  same  manner  round 
its  ends  ;  and  if  fillets  be  placed  under  this  fillet, 
whose  fironts  stand  a  little  within  the  firont  of  the 
upper  fillet,  but  projecting  beyond  the  face  of  the 
architrave  and  the  ends  of  these  fillets,  in  the  same 
plane  with  the  sides  of  the  triglyph,  and,  conse- 
quently, each  fillet  equal  in  length  to  the  breadth  of 
the  triglyph ;  and  if  under  each  of  these  fillets  be 
fixed  six  equal  similar  finistums  of  cones,  at  equal 
distances  from  each  other,  whose  axes  are  perpen- 
dicular to  the  horizon,  and  the  same  distance  from 
the  face  of  the  architrave,  so  that  the  extremities  of 
these  frustums  may  not  reach  beyond  the  perpen- 
dicular of  the  ends  of  the  fillets  above  them,  —  then 
the  front  of  the  architrave  so  formed  is  called  a 
Doric   architrave. 

9.  The  upper  fillet  of  the  Doric  architrave  is 
called  a  tenia. 

10.  The  fillets  under  the  tenia  of  the  Doric  archi- 
trave are  each  of  them  called  a  regula. 

11.  The  little  conical  finistums  under  each  regula 
are  called  guttce,  or  drops. 


96 


GRECIAN    DORIC. 


12.  The  plain  part  of  the  architrave  under  the 
tenia  and  regute  is  called /acia. 

13.  If  over  the  capitals  of  the  triglyph  be  laid 
another  beam,  whose  front  is  parallel  to  the  metopes 
or  to  the  front  of  the  triglyphs  in  the  frieze,  having  a 
small  projecture  from  the  front  of  the  metopes  ;  and 
if  over  this  beam  be  laid  the  ends  of  the  rafters 
which  support  the  covering,  the  ends  having  a  pro- 
jecture forward  and  parallel  to  the  beam  under  them, 
one  rafter  over  each  triglyph,  and  also  one  over  every 
metope,  placed  directly  in  the  middle  of  each ;  that 
is  to  say,  a  vertical  plane  perpendicular  through  the 
middle  of  every  metope,  and  also  through  the  middle 
of  every  triglyph,  would  pass  through  the  ends  of  all 
the  rafters,  and  divide  them  into  two  equal  rectan- 
gles ;  and  if  over  the  rafters  be  laid  a  beam,  the  front 
of  which,  being  a  plane  parallel  to  the  ends  of  the 
rafters,  has  a  projectiire ;  and  if  the  void  spaces  be- 
tween each  two  rafters  and  the  under  side  of  the 
beam  above  the  rafters  and  the  upper  side  of  the 
beam  below  the  rafters  be  covered  in,  so  that  the 
front  of  the  spaces  so  covered  may  be  in  the  same 
vertical  plane  with  the  face  of  the  beam  under  the 
rafters,  —  then  those  ends  of  the  rafters  projecting  over 
the  face  of  the  beam  under  them  are  called  mutules. 

14.  If  to  the  under  side  of  the  mutules  be  hung 
three  rows  of  small  conical  frustums,  of  the  same 
size  as  those  under  the  regula;  of  the  architrave,  so 
that  there  may  be  six  in  length  in  each  of  the  rows, 
and  three  in  width,  then  these  conical  frustums  are 
also  called  gutta;,  or  drops,  as  those  in  the  archi- 
trave. 

15.  The  front  of  the  beam  lying  over  the  mutules 
is  called  corona,  or  drip,  or  larmier. 

16.  The  under  side  of  the  beam  lying  over  the 
mutules  is  called  soffit,  or  lacunar. 

17.  A  building,  whether  of  wood  or  stone,  or  any 
other  material,  having  columns  supporting  an  entab- 
lature over  them,  as  described  in  the  preceding  defi- 
nitions,—  such  a  building,  so  constructed,  is  said  to 
be  of  the  Doric  order. 

Having  defined  the  principal  parts  of  this  order,  it 
may  not  be  improper  to  observe  that  the  Doric  order 
lias,  in  general,  more  mouldings  in  the  cornice  ;  but 
;is  these  vary  in  different  buildings,  and  as  the  mem- 
bers already  described  form  its  most  striking  features, 
i,  would  have  been  useless  to  have  taken  any  ac- 
i;,;int  of  them  in  the  definitions. 


PROBLEM   I 

To    draw   the   elevation    of    a   Grecian    Doric 
order. 

Make  the  lower  diameter  of  the  shaft  of  the  col- 
umn one  eighth  of  the  entire  heiglit  of  the  order; 
divide  the  diameter  of  the  column  into  two  equal 
parts ;  then  one  of  these  parts  is  a  module ;  divide 
the  module  into  thirty  equal  parts,  and  each  of  these 
parts  will  be  a  minute ;  make  the  height  of  the  col- 
umn twelve  modules,  the  height  of  the  capital  one 
module ;  divide  the  height  of  the  capital  into  five 
equal  parts  ;  give  one  to  the  hypotrachelion,  and  two 
parts  to  the  annulets  and  echinus ;  make  the  annu- 
lets one  quarter  of  the  echinus,  and  the  remaining 
two  parts  to  the  abacus ;  make  the  upper  diameter 
of  the  shaft  three  quarters  of  the  lower  diameter  of 
the  shaft,  the  length  of  each  side  of  the  abacus  two 
modules  and  one  fifth,  or  two  modules  and  twelve 
minutes ;  the  height  of  the  entablature  will  be  four 
modules,  of  which  the  height  of  the  cornice  will 
have  one  module,  and  the  frieze  and  architrave  each 
forty -five  minutes,  or  one  module  and  a  half;  divide 
the  height  of  the  frieze  into  eight  parts ;  give  the 
upper  one  to  the  capital  of  the  triglyph,  and  the 
three  lower  for  the  channels  ;  make  one  edge  of  the 
triglyph  in  the  columns  at  the  angles  of  the  building, 
directly  over  the  axis  of  the  column,  the  breadth  of 
the  triglyph  tAventy-eight  minutes,  having  the  other 
edge  of  the  triglyph  dncctly  at  the  angle  of  the 
building ;  and  make  the  distance  between  the 
triglyph,  or  width  of  the  metopes,  equal  to  the  height 
of  the  frieze,  forty-two  minutes ;  place  all  the  col- 
umns between  the  two  extreme  ones  directly  under 
the  middle  of  the  triglyphs.  Make  the  height  of  the 
tenia  one  tenth  of  the  height  of  the  epistilium ;  and 
the  height  of  the  regula,  together  with  tlic  guttae, 
equal  to  the  height  of  the  tenia.  The  height  of  the 
cornice  being  one  module,  make  tlie  height  of  the 
small  bead  on  the  lower  part  of  the  cornice  one  min- 
ute ;  the  height  of  the  mutules,  including  the  guttse, 
four  minutes  and  a  half;  the  length  of  tlie  mutules 
equal  to  the  breadth  of  the  triglyplis,  and  their  pro- 
jection beyond  the  faces  of  the  triglyphs  two  thuds  of 
their  length,  observing  that  one  should  be  directly 
over  the  middle  of  every  triglyph,  and  one  over  the  mid- 
dle of  every  metope ;  make  a  fillet  above  the  mutules 


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GRECIAN    DORIC. 


97 


one  minute  and  a  half  higli,  to  project  beyond  the 
mutules  half  a  minute  over  this  fillet;  make  the 
height  of  the  corona  one  third  of  a  module,  or  ten 
minutes,  having  a  projccture  over  the  fillet  one  min- 
ute ;  make  the  height  of  the  small  echinus  one  min- 
ute and  a  quarter ;  over  the  echinus  make  a  fillet  of 
the  same  height ;  over  the  fillet  make  another  echi- 
nus six  minutes  and  a  half  high,  and  two  minutes 
will  remain  for  the  height  of  the  fillet  above  the 
echini;.-?. 

In  order  to  establish  the  proportions  and  true  taste 
of  the  original  Doric  order,  the  following  examples 
are  taken  from  the  most  celebrated  biiildings  now 
remaining  of  this  order.  The  module  is  divided  into 
thirty  parts,  or  minutes ;  the  measures  are  all  num- 
bered in  these  parts ;  the  projections  are  reckoned 
from  a  line  representing  the  axis  of  the  column,  and 
are  figured  at  the  extremities  of  each  member. 

Plate  44. 

ELEVATION-  OF  THE  DORIC  ORDER  ON  THE  TEMPLE 
OF  MINERVA,  AT  ATHENS,  CALLED  RARTHENON. 

This  temple,  dedicated  to  Minerva,  the  chief  god- 
dess of  the  Athenians,  is  the  most  beautiful  piece  of 
antiquity  remaining.  It  was  built  by  Pericles,  who 
employed  Ictimus  and  Callicrates  for  his  architects. 
The  entablature  is  charged  with  historical  figures  of 
admirable  workmanship  ;  the  figures  of  the  pediment, 
though  seen  at  so  gi-eat  a  height,  appear  to  be  as 
large  as  life,  being  in  alto  rilicvo,  and  well  executed ; 
the  figure  in  the  middle  seems  to  have  been  made 
for  Jupiter,  its  right  arm  being  broken  off,  which  prob- 
ably held  the  thunder.  It  is  likely  that  between  his 
legs  was  placed  the  eagle  ;  for  the  beard,  and  majesty, 
and  expression  of  his  countenance,  and  the  figiu-e 
being  naked,  as  he  was  usually  represented  by  the 
Greeks,  sufficiently  show  it  to  have  been  made  for 
Jupiter.  At  his  right  hand  is  another  figure,  covered 
half  way  down  the  legs,  coming  towards  him,  which 
perhaps  was  a  Victory,  leading  the  horses  of  INIiner- 
va's  triumphal  chariot,  which  follows  it.  The  horses 
are  finished  with  great  art ;  the  vigor  and  spirit  pe- 
culiar to  those  animals  seem  here  to  receive  addition, 
as  if  inspired  by  the  goddess  they  chew.  Minerva,  in 
the  chariot,  is  represented  as  the  goddess  of  learning 
rather  than  of  war,  without  helmet,  buckler,  or  a  Me- 
dusa's head  on  her  breast,  as  Pausanias  describes  her 
image  within   the   temple.      Behind  her  is  another 

13 


figure  of  a  woman  sitting.  The  next  two  figures  in 
the  corner  are  the  Emperor  Hadrian,  and  his  empress 
Sabina.  On  the  left  hand  of  Jupiter  are  five  or  six 
figures,  which  appear  to  be  an  assembly  of  the  gods, 
where  Jupiter  introduces  Minerva,  and  acknowledges 
her  his  daughter. 

The  pediment  at  the  other  end  of  the  temple  was 
adorned  with  figures,  expressing  Minerva's  contest 
with  Neptune  about  who  should  name  the  city  of 
Athens,  of  which  there  only  remains  a  part  of  a  sea 
horse. 

The  frieze  is  charged  with  basso  rilievos,  of  excel- 
lent workmanship,  on  which  are  represented  the  bat- 
tles of  the  Athenians  with  the  Centaurs ;  these  appear 
to  be  as  old  as  the  temple  itself. 

Within  the  portico  on  high,  and  on  the  outside  of 
the  cella  of  the  temple,  is  another  border  of  basso 
rilievos  around  it,  at  least  on  the  north  and  south 
sides  of  it,  which  is  without  doubt  as  ancient  as  the 
temple,  and  of  admirable  workmanship,  but  not  in 
so  high  a  rilievo  as  the  other.  On  it  are  represented 
sacrifices,  processions,  and  other  ceremonies  of  the 
heathen  worship. 

This  temple  is  now  turned  into  a  Turkish  mosque. 

Fig.  1.  Elevation  of  the  Doric  order ;  the  propor- 
tions of  the  parts  m  numbers. 

Fig.  2  is  a  design,  showing  the  order,  with  the  col- 
umn and  entablature  entire. 

Plate  45. 

Fig.  1.  This  example  shows  the  return  of  the  flank 
at  the  angle  of  the  building.  The  figm-es  in  the 
metope  are  omitted. 

Figs.  2  and  3  show  the  forms  of  the  moulding  and 
upper  part  of  the  cornice. 

Fig.  4.  Elevation  of  the  capital,  and  of  striking 
the  ovolo  by  conic  sections. 

Fig.  5.    Section  of  one  half  the  column. 

Fig.  6.  Section  tlu'ough  the  annulets,  of  a  large 
size. 

Fig.  7.    Plan  of  the  soffit  inverted. 

Plate  46. 

ELEVATION  OF  THE  DORIC  ORDER  ON  THE  TEMPLE 
OF  THESEUS,  AT  ATHENS. 

This  temple  is  one  of  the  most  ancient  examples 
of  the  Doric  order  now  existing ;  it  was  erected  about 
ten  years  after  the  battle  of  Salamis,  by  Cimon,  the 
son  of  Miltiades.     The  ceiling  of  the  porch  is  re- 


98 


GRECIAN    IONIC. 


markable  for  its  construction  ;  there  are  great  beams 
of  marble,  the  upper  sides  of  which  are  level  with  the 
bed  of  the  cornice,  and  the  ends  corresponding  ex- 
actly to  the  triglyphs  in  the  frieze,  which  give  the 
idea  of  the  disposition  of  the  timbers  which  were 
first  used  in  buildings,  and  from  which  the  Doric 
order  is  said  to  have  had  its  origin. 

This  buUding  is  adorned  with  beautiful  sculpture  ; 
the  metopes  of  the  frieze  are  charged  with  historical 
figures,  on  which  are  represented  various  exploits  of 
Theseus ;  the  battle  he  had  with  Sinis,  the  notorious 
robber,  who  dwelt  in  the  Isthmus  of  Corinth.  The- 
seus is  represented  making  Sinis  undergo  those  tor- 
ments which  he  had  inflicted  on  others. 

In  the  basso  rilievo  is  represented  a  man  taking 
hold  of  another  by  his  middle,  and  endeavoring  to 
throw  him  down  ;  this  is,  doubtless,  intended  to  rep- 
resent Theseus  throwing  Sch-on  from  a  rock;  the 
combat  of  Theseus  with  the  wild  sow  of  Crommyon, 
which  was  killed  by  that  hero.  In  another  basso 
rilievo  is  represented  a  man  presenting  his  hand  to 
a  woman,  perhaps  to  express  the  rape  of  Ai-iana,  or 
Helen,  by  Theseus. 

Some  others  of  the  basso  rilievos  in  the  metopes 
are  less  distinguished.  The  two  mentioned  by  Pau- 
sanius  arc  still  to  be  seen  on  the  front  of  the  temple  ; 
one  represents  the  battle  of  the  Athenians  with  the 
Amazons,  the  other  the  dispute  of  the  Centam-s  and 
the  Lapithw,  in  which  Theseus  kills  a  Centaur  with 
his  own  hand. 

The  first  seems  to  represent  the  instant  when  the 
Athenians  granted  peace  to  the  Amazons,  for  there 
the  women  are  represented  as  sitting. 

The  inside  of  the  temple  is  not  ornamented  like 
the  outside. 

This  temple  is  now  a  Greek  church,  dedicated  to 
St.  George,  and  is  at  present  in  high  esteem  among 
the  Athenians. 

Fig.  1.  The  elevation  of  the  order,  with  the  heights 
and  projections  of  the  members  in  numbers. 

The  figures  in  the  metopes  are  omitted. 

Fig.  2.  Represents  the  ovolo  above  the  facia  of 
the  cornice. 

Fig.  3.    Plan  of  the  sofilt  inverted. 

Fig.  4.  Plan  of  the  ovolos  and  annulets  of  the 
column. 

Fiff.  5.    Section  of  one  half  of  the  column. 


Plate  47. 

ELEVATION  OF  A  URECIAX  DOHIC,  OF  A  LIGHTER 
PUOrOKTIOX  THAN  ANY  OF  THE  I'KECEDIXG,  WITU 
THE   PIlOrORTIOXAL   MEASURES  IX  NUMBERS. 

The  ratio  of  the  parts  of  this  elevation  is  the  same 
as  that  on  the  portico  of  Philip,  King  of  Macedon,  in 
the  Island  of  Delos ;  but  the  profile  of  the  cornice 
diflcrs  as  follows :  Instead  of  the  ovolo,  which  I  have 
introduced  in  this  example,  a  cima  recta  in  the  origi- 
nal occupies  its  place  ;  and  instead  of  the  next  ovolo 
under  the  fillet  in  this,  there  is  in  the  original  a  cima 
rcversa.  The  profile  in  this  plate  I  conceive  to  be 
more  beautiful  than  the  original,  as  it  will  produce  a 
greater  variety  of  light  and  shade,  and,  consequently, 
the  mouldings  will  be  more  clearly  defined  ;  but  as 
the  reader  may  be  desirous  of  a  knowledge  of  the 
true  form  and  taste  of  the  original  mouldings,  I  have 
shown  them  in  Fig.  3. 

Fig.  1.  Elevation,  with  the  jiroportional  measures 
in  numbers. 


Fig.  2.    A  section  through  the 


upp 


er  part  of  the 


cornice,  showing  the  form  and  taste  of  the  mouldings 
inti'oduccd  into  this  elevation,  by  P.  Nicholson. 
Fig.  4.    A  section  of  the  anta3  of  the  same  portico. 

Plate  48. 

FROM  THE  CHGRAGIC  MONUMENT  OF  THRASYLLUS. 

Fig.  1.    The  proportional  measm-es  in  irumber. 
Fig.  2.    Section  through  the  cornice. 
Fig.  3.    Section  throvigh  the  capital. 


GRECIAN     IONIC. 

Plate   49. 

THE   IONIC    TEMPLE. 

Fig.  1.  A  grouml  plan  of  the  Temple  on  the  Ilissu.'!,  irith  a  por- 
tico at  each  end.  The  colums  G  G  are  wanting  ;  but  in  the  place 
•where  they  stood  circles  are  marked  on  the  pavement,  which  are 
exactly  of  the  same  dimensions  with  the  remaining  columns,  and 
were  evidently  designed  as  an  accurate  guide  to  the  workmen,  when 
they  erected  those  columns  which  are  now  destroyed  ;  for  wliich 
reason  it  was  thought  necessary  to  make  these  circles  like\rise  on 
the  plan  which  is  here  given.  The  capitals  of  the  antip,  belonging 
to  the  posticus  or  back  front,  remain  entire,  and  are  of  the  same 
form  and  dimensions  with  those  of  the  portico,  except  only  that  the 
sides  contiguous  to  the  hack  wall  of  the  cell  are  but  half  so  broad 
as  the  faces  next  to  the  columns ;  whereas,  in  the  antce  oi  the  por- 


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VLJ 


GRECIAN    IONIC. 


99 


tico,  the  sides  next  tlie  pronaos  and  the  faces  next  the  columns 
are  equal.  The  architraves  of  the  back  front  project  considerably 
beyond  the  ant;c,  and  there  arc  sufficient  remains  of  them  to  show 
exactly  how  far  the  columns  of  the  back  front  were  distant  from 
the  back  wall  of  the  cell. 

Fig.  2.  The  elevation  of  the  south  side  of  the  temple. 

Note.  —  The  ground  plan  and  elevation  are  here  given  as  meas- 
ured by  Stuart  and  Ilcvctt,  in  feet,  inches,  and  decimals. 

It  has  been  already  observed,  in  the  general  definitions  of  the 
orders,  that  every  order  consists  of  a  column  and  an  entablature ; 
that  every  column  consists  of  a  base,  a  shaft,  and  a  capital,  except 
in  the  Doric,  where  the  base  is  omitted ;  that  every  entablature  con- 
sists of  an  architrave,  a  frieze,  and  a  cornice ;  that  the  base,  shaft, 
capital,  architrave,  frieze,  and  cornice  are  the  principal  members  of 
an  order ;  and  that  the  peculiar  mode  or  form  of  the  members  de- 
termines the  particular  name  of  the  order.  But  since  many  of  the 
mouldings  are  common  to  all  the  orders,  and  are  generated  in  a 
similar  manner,  what  has  been  said  in  the  general  definition,  and 
also  on  the  Doric  order,  will  render  it  unnecessary  to  repeat  the 
same  things  in  the  Ionic,  as  such  mo\ildings  cannot  form  any  partic- 
ular feature  of  any  particular  order.  It  is  therefore  sho\vn,  in  the 
subjoined  definitions,  how  these  members  ought  to  be  modified,  so 
that  they  may  constitute  the  Ionic  order. 


DEFINITIONS. 

1.  If  from  the  under  side  of  the  abacus  of  an  or- 
der there  project  two  or  more  sphals  on  each  end  of 
the  fi'ont,  in  a  plane,  parallel  to  the  frieze,  so  that  the 
extremity  of  each  shall  be  at  the  same  distance  from 
the  axis  of  the  column,  and  also  two  others  upon  the 
opposite  side  of  the  abacus,  parallel  to  the  former 
and  projecting  the  same  distance  from  the  axis  of  the 
column,  so  that  each  of  the  spirals  shall  have  the 
same  number  of  revolutions,  and  equal  and  similar  to 
each  other,  the  projecting  part  contained  between 
any  two  spirals  is  called  a  volute. 

2.  An  order  which  has  volutes  and  mouldmgs  in 
the  capital  of  the  annular  kind,  and  the  ichnogi-aphy 
of  the  abacus  square,  as  in  the  Doric  order,  the  archi- 
trave finishing  of  plain  facia?,  and  mouldings  either 
plain  or  enriched,  the  frieze  a  plain  surface,  the  cor- 
nice to  consist  of  a  cima  recta,  then  a  fiJlet  and  an 
echinus  only ;  and  if  to  the  under  side  of  the  corona 
are  hung  a  row  of  equal  and  similar  parallclopipeds, 
equidistant  from  each  other,  whose  fronts  arc  in  a 
plane  parallel  to  the  plane  of  the  frieze,  then  each  of 
these  parallclopipeds  is  called  a  dentil. 

3.  An  order  so  constructed  is  similar  to  that  in- 
vented by  the  lonians,  and,  consequently,  is  the  Ionic 
order. 


Plate  30. 

FROM  THE    IONIC  TEMPLE    ON    THE    lUYER    ILISSUS, 
AT    ATHENS. 

The  simplicity  and  greatness  of  the  parts,  their 
judicious  arrangement,  the  beautiful  turning  on  the 
volutes,  and  the  graceful  curve  of  the  hem  hanging 
between  tliem,  render  this  one  of  the  most  beautiful 
and  bold  examples  of  this  order. 

The  elegant  base  of  the  column,  the  grand  propor- 
tion of  the  entablature,  the  massy  mouldings  of  the 
cornice,  and  the  spacious  surface  of  the  frieze,  well 
adapted  for  sculptured  ornaments,  and  the  architrave 
for  its  strength,  as  it  is  not  broken  in  two  or  more 
facia;,  arc  considerations  which  shoidd  recommend 
this  example. 

Fig.  1.  The  elevation  of  the  order  and  details  fig- 
ured in  proportional  parts  for  practice. 

Fig.  2.  A  drawing  of  the  order,  by  dividing  the 
whole  height  into  twenty-one  parts,  which  are  dis- 
posed of  in  modules  and  mmutes,  as  shown  in  the 
example  ;  one  of  the  parts  makes  a  module,  or  thirty 
minutes. 

Fig.  3  shows  how  to  form  the  curve  of  the  fluting ; 
the  Grecians  used  the  ellipsis  form,  while  the  Ro- 
mans as  uniformly  made  use  of  a  semicucle,  as  in 
Fig.  4. 

Fig.  4.  Explained  the  same  as  Fig.  3,  in  plate  58. 


Fi£ 


Plate  51. 

1.  The  capital  inverted,  of  the  different  tastes 


of  forming  the  volutes. 

Fig.  2.  The  elevation  of  the  same. 

Plate   52. 

FROM  THE  TEMPLE  OF  mXERVA  POLIAS,  AT  PRIENE, 
IX  IONIA. 

The  small  projection  of  the  cima  recta,  and  its 
great  height,  is  of  itself  beautiful  and  well  contrived 
for  the  ornament,  as  it  is  less  obsciircd  by  the  shadow 
from  the  concave  and  convex  parts  of  the  moulding. 
This  small  projecture  is  also  well  adapted  for  a  low 
corona ;  for  the  greater  the  projecture  of  the  cima 
recta,  the  more  it  will  predominate  over  the  corona, 
by  the  principles  of  optics  ;  and,  on  the  contrary,  the 
less  the  projecture  of  the  cima  recta,  the  less  it  will 
predommate  over  the  corona.  It  follows,  therefore, 
that  a  low  corona  wiU  require   a   cima  recta  of  a 


100 


GRECIAN    IONIC. 


small  projccture;  but  a  gi-eater  height  of  the  corona 
will  require  a  greater  projecture  of  the  cima  recta, 
and  a  less  height.  The  dentils,  which  are  a  striking 
feature  in  this  order,  show  here  to  very  great  advan- 
tage, their  bold  and  singular  projecture  greatly  reliev- 
ing tlicm  from  each  other. 

The  architrave  is  well  proportioned  to  itself,  and 
also  to  the  cornice ;  the  capital  is  elegant,  and  the 
spirals  of  the  volutes  arc  beautifully  drawn. 

The  surprising  delicacy  of  the  ornaments,  and  thck 
bold  relief,  with  the  grand  ratio  of  the  parts  and 
mouldings  to  each  other,  I'cnder  this  one  of  the  most 
beautiful  examples  of  the  Ionic  order. 

Fig.  1.  The  elevation  of  this  example,  the  propor- 
tional measures  in  numbers. 

Fig.  2.  Ichnography  of  the  dentils. 

Fig.  3.  Profile  of  the  mouldings  in  the  base  to  a 
larger  size. 

The  cimatium,  or  crown  of  the  arcliiti-ave,  was 
taken  from  the  designs  of  Mr.  Wood,  who  visited 
this  temple  before  Mr.  Revett. 

The  base  of  the  column  is  true  Ionic :  it  has  no 
plinth ;  the  upper  scotia  is  inverted,  which  diversifies 
and  gives  the  contoiu*  a  greater  beauty  than  is  the 
Vitruvian  base,  in  which  the  scotiaj  are  one  over  the 
other,  uninvertcd.  The  torus  is  elli2:)tical,  and 
fluted. 

The  eyes  of  the  volutes  are  bored  two  inches  and 
a  half  deep ;  the  hem,  or  border,  with  its  fillets  rest- 
ing on  the  echinus,  and  connecting  with  a  gi-aceful 
curve  the  spirals  of  the  volutes,  seeming  to  keep 
them  secure  in  their  place,  adds  greatly  to  the  beauty 
of  this  capital. 

Plate  53. 

FROM  THE  TEMPLE  OF  MINERVA  POLIAS,  AT  RRIENE. 

Fig.  1.  Section  through  the  cornice  of  the  pediment. 

Fig.  2.  Front  of  tlie  cornice,  showing  the  orna- 
ments on  the  mouldings.  It  is  remarkable,  that  the 
enrichment  of  the  upper  moulding  dificrs  from  that 
on  the  lateral  cornice. 

Fig.  3.  The  mouldings  of  the  capital,  with  then- 
proportion  in  numbers. 

Fig.  4.  Volute,  with  the  measure  in  feet,  inches, 
and  tenths. 


Fig.  5.  A  section  through  the  upper  torus  of  the 
base,  which  is  of  an  elliptical  form,  the  transverse 
axis  being  inclined  to  the  plane  of  the  horizon. 

Plate  54. 

FROM   THE   SAME   TEMPLE. 

Fig.  1.  The  elevation  of  the  front  of  the  capital, 
to  larger  size. 

Fig.  2.  The  ichnography  of  half  of  the  capital. 
Fig.  3.  Side  elevation  of  the  same. 

Plate  55. 

FROM  THE  TEMPLE  OF  BACCHUS,  AT  TEOS,  IN  IONIA. 

This  temple  was  first  begun  of  the  Doric  order,  by 
Hermogenus  ;  but  afterwards  he  changed  it  into  the 
Ionic,  and  dedicated  it  to  Bacchus. 

This  example  is  drawn  from  accurate  measures, 
taken  from  that  celebrated  building. 

The  dentils,  in  the  cornice,  add  gi-catly  to  the  char- 
acter of  the  order. 

Fig.  1.  The  elevation  of  the  order.  It  may  here 
be  observed,  that  no  measiues  have  been  taken  of 
the  parts  which  are  marked  in  this  example  with 
letters,  as  none  of  them  could  be  found.  They  arc 
here  supplied  by  mere  conjectTire. 

The  base  of  the  columns.  It  is  thought,  from  the 
little  differences  between  the  shaft  at  the  base  and 
that  immediately  under  the  capital,  that  the  base 
which  is  here  exhibited  did  not  belong  to  the  capital 
shown  at  Fig.  l,but  to  some  of  the  interior  columns; 
for  the  ancients  always  made  the  interior  ranges  of 
columns  less  in  diameter  than  the  exterior,  as  is  to 
be  found  in  the  celebrated  Athenian  buildings,  the 
Temple  of  Minerva,  and  the  Propylea. 

Fig.  2.  Profile  of  one  half  the  fi-ont  of  the  capital, 
with  the  measure  of  the  volute,  and  proportional 
measures  in  numbers. 

Plate  56. 

FROM  THE  TEMPLE  OF  MINERVA,  AT  ATHENS. 

Fig.  1.  Another  example  of  a  volute,  showing  the 
different  sections  and  formation  of  the  face  mould 
ings  thereof. 

Fig.  2.   A  section  through  A  B. 


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GRECIAN    ARCHITECTURE. 


101 


GRECIAN     AllCHITECTURE. 

CORINTHIAN   ORDER. 

On  the  archih-avc  of  the  Choragic  Monument  at  Lysicrates  was 
the  following  inscription :  — 

"  Lysicrates,  of  Kikyna,  the  son  of  Lisithetdcs,  teas  citoraffiis,  (or  gave 
the  chorus  at  his  own  expense.)  T/ie  tribe  of  Akamantis  obtained 
tlte  victory  in  the  chorus  of  boys.  T/ieon  teas  the  performer  on  the  flute  ; 
Lysades,  an  Athenian,  was  the  teacher  of  the  chorus.  Eeaenatus  was 
archon." 

From  this  we  conclude  that  on  some  solemn  festival,  which  was 
celebrated  with  games  and  plays,  Lysicrates  of  Kikyna,  a  demos 
or  borough  town  of  the  tribe  of  Akamantis,  exhibited  at  his  own 
expense,  on  behalf  of  the  tribe  to  which  he  belonged,  a  musical  or 
theatrical  entertainment,  in  which  the  boys  of  Akamantis  obtained 
the  ■(■ictory  ;  also,  that,  in  commemoration  of  the  victory,  this  mon- 
ument was  erected  to  perpetuate  the  same  to  posterity,  by  the  name 
of  the  archon,  or  magistrate,  in  whose  time  this  took  place.  It  ap- 
pears that  the  buUding  was  erected  about  three  hundred  and  thirty 
years  before  the  Christian  era,  in  the  time  of  Demosthenes,  ApeUcs, 
Lysippus,  and  Alexander  the  Great.  The  tripod  seems  to  have 
been  the  peculiar  reward  bestowed  by  the  people  of  Athens  on  that 
choragus  who  exhibited  the  best  musical  or  theatrical  entertain- 
ment ;  and  we  find  this  particular  custom  obtained  for  these  tripods 
the  name  of  choragic  tripods.  It  was  customary  for  the  victor  to 
dedicate  the  tripod  he  had  won  to  some  divinity,  and  to  place  it 
either  on  one  of  the  temples  abrcady  built,  or  on  the  top  of  some 
edifice  erected  and  consecrated  by  him  for  the  purpose.  Tlius  they 
participated  of  the  sanctity  of  the  place,  and  were  secured  from  in- 
jury or  violence. 

A  tripod  thus  dedicated  was  always  accompanied  with  an  inscrip- 
tion, so  that  it  became  a  permanent,  authentic,  and  public  monu- 
ment of  the  victory  and  of  the  person  who  had  obtained  it. 

Stuart  and  Eevett  deduce  many  circumstances  to  prove  that  it 
was  erected  for  the  above  purpose,  which  appears  rational  and 
conclusive. 


Description  of  the  Choragic  Monument. 

The  Choragic  JMonviment  of  Lysicrates,  which  we 
are  about  to  describe,  is  commonly  called,  by  the  mod- 
ern Athenians,  to  *ava|i  tou  Arnxotfl^vioj,  or  the  Lantern 
of  Demosthenes. 

This  monument  of  antiquity,  which  is  exquisitely 
\\Tonght,  stands  near  the  eastern  end  of  the  Acropo- 
lis, and  is  partly  enclosed  in  the  hospitium  of  the 
Capuchins.  It  is  composed  of  three  distinct  parts : 
first,  a  quadrangular  basement ;  secondly,  a  circular 
colonnade,  of  which  the  intercolumniations  were  en- 
tirely closed ;  and  thirdly,  a  tholus,  or  cupola,  with  the 
ornament  that  is  on  it.  There  is  no  entrance  or  aper- 
ture in  the  basement,  which  is  entirely  closed  on 
every  side.  The  basement  supports  the  circidar  col- 
onnade, and  was  constructed  in  the  following  man- 
ner :    SLx  equal  panels  of  white  marble  placed  con- 


tiguous to  each  other,  on  a  circular  plan,  formed  a 
continued  cylindrical  wall,  wlxich  was  divided  from 
top  to  bottom  into  sL\  equal  parts  by  the  junction  of 
the  panels.  On  the  whole  length  of  each  juncture 
was  cut  a  semicircular  gi-oove,  into  which  a  Corin- 
thian column  was  fitted  with  great  exactness,  so  as 
eflcctually  to  conceal  the  junctures  of  the  panels.* 
These  columns  projected  somewhat  more  than  half 
their  diameters  from  the  surface  of  the  cylindrical 
wall,  and  have  the  Attic  base.  The  shaft  of  the  col- 
umn is  fluted  in  a  singular  manner ;  it  contains  thir- 
teen flutes :  the  lower  extremities  of  these  flutings 
descend  below  their  usual  limits,  and  are  cut  into  the 
apophyges,  or  scape  of  the  column,  and  the  upper 
extremities  terminate  in  the  form  of  leaves ;  the  an- 
nular channel,  immediately  above  them,  which  di- 
vides the  shaft  of  the  column  from  the  capital,  waa 
probably  filled  with  an  astragal  or  collarino  of  bronze. 
Under  this  terminated  the  fluting  in  the  form  of  an 
annular  tier  of  leaves,  turning  outward  from  the  shaft 
of  the  column. 

This  capital  exhibits  a  specimen  of  the  Grecian 
art.  The  annular  tier  of  leaves  springing  from  the 
neck  in  fonn  of  the  palm,  the  acanthus  forms  the 
second  tier  with  the  flowers.  Li  the  third  tier  is 
shown  the  beautiful  branches  and  the  scrolls,  termi- 
nating under  the  angular  extremity  of  the  abacus, 
the  points  of  which  are  cut  short ;  it  in  this  respect, 
as  well  as  in  the  disposition  of  the  foliage,  differs  con- 
siderably from  any  other  example  of  the  Grecian 
Corinthian  capitals. 

The  entablature.  The  architrave  is  divided  into 
four  divisions,  the  band  or  ogee  and  three  parallel 
planes  or  faces  projecting  one  over  the  other ;  the 
lower  edges  stand  out  one  or  two  degrees  from  a  per- 
pendicular line. 

The  frieze  of  this  entablature  is  ornamented  with 
sculpture,  representing  the  story  of  Bacchus  and  the 
Tyrrhenian  pirates.  The  figure  of  Bacchus  himself, 
the  fauns  and  the  satyrs  who  attended  on  the  mani- 
festation of  his  divinity,  the  chastisement  of  the 
pirates,  their  terror  and  their  transformation  into  dol- 
phins, are  expressed  in  this  basso  riUevo  with  great 
spirit  and  elegance. 

The  cornice  is  very  plain,  composed  of  dentils  and 


*  The  two  tripods  are  -wrought  in  basso  rilievo  on  each  of  the 
panels ;  they  are  probably  of  the  kind  described  by  Homer  and 
Hesiod. 


102 


BASES. 


plain  moiUduigs,  in  the  place  of  the  cima  or  cima- 
tium,  having  an  upright  front ;  it  is  ornamented  with 
scrolls  and  honeysuckle  foliage  in  basso  rUievo,  in 
the  Yitruvian  style.  This  cornice  is  composed  of 
several  pieces  of  white  marble,  and  bound  together 
by  a  cupola  of  one  entire  piece. 

The  cupola  is  ornamented  with  elegant  workman- 
ship ;  its  covering  imitates  that  of  thatch  or  of  laurel 
leaves  ;  the  turret  standing  du-cctly  over  the  wall  re- 
sembles a  Vitruvian  scroll ;  next  above  the  lam-el 
leaves,  the  covering  of  the  dome,  spring  three  scrolls, 
at  equal  distances  from  each  other,  in  imitation  of 
those  branches  in  the  capital  shown  in  this  plate. 
The  flowers  that  ornament  the  top  rise  from  the  cen- 
tre, and  are  composed  of  workmanship  of  foliage, 
which  terminate  in  three  divisions  of  scrolls,  of  great 
richness,  on  the  top  of  which  it  is  believed  was  sup- 
ported the  tripod  gained  as  the  prize,  from  the  ck- 
cumstancc  that  cavities  are  cut  on  the  three  principal 
projections  in  an  equilateral  triangle,  into  which  the 
feet  of  the  tripod  were  probably  fixed ;  and  in  the 
fourth  cavity,  which  is  in  the  centre,  and  much  the 
largest,  was  erected  a  baluster  to  support  the  tripod. 
Plate  57. 

Fig.  1.  This  figure  represents  the  elevation  of  the 
Grecian  Corinthian  order,  from  the  Choragic  Monu- 
ment of  Lysicrates,  proportioned  to  modules  and 
minutes. 

Fig.  2.    The  inverted  projection  of  the  cornice. 

Fig.  3.    The  base  is  attached  to  the  basement. 

Fig.  4.    The  capital  inverted. 

Plate  3S. 

To  draw  the  flutes  of  the  columns  of  the  Doric 
order. 

Divide  the  semi-circumference  into  ten  equal  parts ; 
then  with  one  of  those  parts,  as  a  radius,  and  the 
extremities  of  any  division,  as  at  3  and  4,  describe 
arcs,  cutting  each  other  in  C,  and  through  C  describe 
a  circle,  or  a  part,  and  draw  lines  from  the  centre, 
cutting  that  circle,  which  will  give  the  centres  for  de- 
scribing the  flutes. 

Or  thus,  for  deeper  Flutes. 

Bisect  any  division,  as  5,  6,  at  /;  then  on  5, 
with  the  distance  5  /,  describe  an  arc  /  D,  cutting 
the  radius  produced  through  5  at  D,  and  draw 
the  radii  through  the   points  5,  6,  7,  8,   9,  10,  cut- 


ting that  circle,  which  will  give  the  centies  of  the 
flutes. 

Fig.  2.    The  elevation  drawn  from  the  plan.  Fig.  1. 


To  ckaw  the  flutes  of  the  Ionic  and  Corinthian 
orders. 

Fig.  3.  Divide  the  semi-circumference  into  twelve 
equal  parts ;  divide  any  division,  as  between  5  and 
6,  into  eight  equal  parts ;  then  with  a  radius  of  three 
of  these  equal  parts,  on  the  points  1,  2,  3,  4,  5,  6,  7, 
8,  9,  10,  11,  12,  as  centres,  describe  the  flutes,  which 
will  leave  the  fiUets. 

Fig.  4.    The  elevation  drawn  from  the  plan.  Fig.  3. 


BASES. 

In  no  example  of  antiquity  is  the  Doric  column  provided  Tvith  a 
base.  Tliis  circumstance,  says  Mr.  Partington,  has  occasioned  no 
small  perplexity  to  some  of  those  'vrriters  -n-ho  seek,  in  every  point, 
some  analogy  to  the  human  figure.  Vitruvius  has  indeed  said  that 
the  base  is  a  slioc,  first  invented  to  cover  the  nakedness  of  the  ma- 
tronly prototyjie  of  the  Ionic  order.  "  But,"  says  Monsieur  Lc  Clcrc, 
"I  must  o^^•n  I  cannot  consider  a  column  without  a  base,  comparing 
it  to  a  man ;  but  I  am,  at  the  same  time,  struck  'with  the  idea  of  a 
person  ■without  feet,  rather  than  without  shoes  ;  for  ■which  reason, 
I  am  inclined  to  believe,  either  that  the  architects  liad  not  yet 
thought  of  employing  bases  to  their  columns,  or  that  they  omitted 
them  in  order  to  leave  the  pavement  clear,  the  angles  and  projec- 
tions of  bases  being  stumbling-blocks  to  passengers,  and  so  much 
the  more  troublesome,  as  the  arcliitects  of  those  times  frequently 
placed  their  columns  very  near  each  other,  so  that,  had  they  been 
made  ■with  bases,  the  passages  between  them  ■^•ould  have  been  ex- 
tremely narrow  and  inconvenient."  To  supply  this  defect,  as  it  is 
generally  considered,  most  architects  have  employed  the  Allic  base, 
which  is  common  to  all  the  orders  except  the  Tuscan,  though  be- 
longing, perhaps,  more  peculiarly  to  the  Ionic.  We  have,  therefore, 
here  given  a  representation  of  it,  as  furnished  by  Mr.  Partington, 
from  Yignola. 

It  is  seen  that  it  consists  of  two  tori, 
with  a  seotia  and  fillets  between,  the 
upper  of  which,  iu  this  version,  resembles 
an  inverted  ovolo.  The  fillet,  above  the 
upper  torus,  is  always  connected  with  the 
shaft  by  a  curve,  as  is  also  that  under  the 
capital,  for  which  reason  they  arc  com- 
monly considered  as  part  of  the  shaft.  The  plinth,  or  square  mem- 
ber beneath,  is  usually  understood,  in  Roman  architecture,  as  an 
indispensable  appendage  to  the  base,  though  PaUadio  has  omitted  it 
in  his  Corinthian  order;  but  it  is  rarely  found  in  the  Greek  speci- 
mens. To  save  tliis  order,  however,  fiom  the  sad  humiliation  of 
being  obliged  to  borrow  a  shoe,  when  required  to  wear  one,  Vignola 
provided  it  with  this  appendage.  Ilis  base  consists  of  one  largo 
torus,  with  one  considerably  smaller  resting  upon  it,  smmountcd 
by  the  fillet. 


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ENTABLATURES. 


103 


M.  Le  Clerc  has,  in  the  opinion  of  Mr.  Partington,  discovered  the 
true  reason  why,  at  least  in  the  latter  Greek  specimens,  the  base  is 
omitted  —  namely,  the  very  narrow  intercolumniations.  In  the 
Greek  order,  alteration  is  not  probable,  and,  perhaps,  not  desirable; 
but  in  the  Roman,  -nhero  this  addition  has  long  been  provided  for 
us,  and  the  intercolumniations  adjusted  accordingly,  the  omission 
would  bo  certainly  improper. 


ROMAN   BASES. 

Several  designs  for  bases  after  the  Roman  taste 
are  given  on  plate  59,  which  may  be  applied  to  col- 
umns, pilasters,  and,  in  some  instances,  to  rooms, 
chimney-pieces,  &c. 

Plate    59. 

Fig.  G.  The  Tuscan  order. 
Fig.  E  and  A.   The  Doric. 
Fig.  B  and  C.  The  Ionic. 
Fig.  D.  The  Corinthian. 


ENTABLATURES. 

The  orders  consist  of  a  composition  of  parts.  When  considered 
in  gross  numbers,  they  consist  of  two  parts,  viz.,  the  column  and 
entablature.  These  divisions  are  subdivided :  the  column  com- 
prises the  base,  capital,  and  their  appendages,  as  shown  in  the  orders. 
The  entablature  consists  of  the  architrave,  frieze,  and  cornice.  The 
architrave,  in  all  the  orders,  has  the  band.  The  Grecian  Doric, 
however,  does  not  furnish  us  with  more  than  two  divisions,  —  the 
band  and  frieze.  The  band,  or  fillet,  which  constitutes  the  upper 
part  of  the  architrave,  is  projected  under  the  trigljiA  ;  and  an  an- 
nulet is  dropped  from  the  iillet,  a  little  on  the  frieze,  to  tlie  soffit  of 
which  are  attached  six  drops,  as  in  the  Grecian  examples. 

In  the  Ionic  and  Corinthian  orders,  the  Greeks  have  divided  the 
frieze  into  three  projecting  parts,  as  sho'^^^l  in  the  example  from  the 
Temple  of  Jlincrva  Polias.  Tlie  divisions  arc,  1st,  lOJ  ;  2d,  12  j ; 
3d,  144  minutes.  The  Romans,  in  this  respect,  have  followed  the 
Greeks,  except  in  the  proportions  of  the  divisions ;  as  seen  in  the 
Doric  elevation  found  at  Albano,  near  Rome;  in  the  Diocletian 
Baths  ;  and  in  the  example  from  Andrea  Palladio. 

2d.  The  frieze  or  entablature  is  ornamented,  in  the  Doric  order, 
with  triglyphs,  and  sometimes  with  sculpture,  as  shown  in  the  ex- 
ample from  the  Temple  of  Theseus,  at  Athens.  Aldrich  has  intro- 
duced triglyphs  into  the  Composite  order,  which  I  consider  a  com- 
position of  the  three  orders.  This  practice,  however,  is  seldom 
adopted  ;  although  there  may  not  be  much  impropriety  in  borrow- 
ing from  the  Doric,  as  well  as  from  the  two  higher  orders. 

The  capital  of  the  triglyph  is  from  4  to  6  minutes  wide.  The 
width  of  the  triglyph  is  commonly  fr-om  28  to  30  minutes,  having  an 
angle  of  135  degrees  from  the  outer  comers,  cutting  from  the  face 
24  minutes.  The  intermediate  space  is  divided  into  five  parts,  the 
second  and  fourth  being  cut  at  right  angles  from  the  centre. 

The  fi'icze  of  the  two  higher  orders,  viz.,  the  Ionic  and  Corinthian, 
afford  a  variety  of  ornaments,  of  which  the  Romans  have  been  very 


profuse  ;  as  on  the  Temple  of  Fortuna  Virilis,  at  Rome.     See  also 
the  example  from  the  Arch  of  Titus. 

3d.  Cornices.  —  This  assemblage  of  parts  affords  much  variety,  from 
the  plain  bed  mould,  mutules,  dentils,  and  modillions.  The  mu- 
tulcs  are  common  in  the  Doric  planceer.  The  dentils  are  common 
in  the  Ionic,  and  are  placed  between  the  hollow  and  the  (juarter 
round,  as  shown  in  the  bed  mould.  An  example  of  this  is  found 
in  the  Temple  of  Fortuna  Vkilis,  and  in  the  Coliseiun,  at  Rome. 
The  quarter  round  is  sometimes  ornamented  with  the  egg  and  dart. 
The  Corinthian  order  has  dentils  and  modillions,  as  shown  in  the 
example  from  Jupiter  Stator.  Tlie  mouldings  are  often  ornamented 
with  carvings  of  various  designs. 

The  facia,  in  the  Grecian  Doric,  projects  from  27  to  30  minutes 
from  the  triglyijhs.  In  the  Roman  Doric,  it  sometimes  projects 
from  34  to  37  minutes.  The  height  of  the  facia  varies  from  7  to  11 
minutes.  The  crown  moulding  is  a  cima  recta,  and,  in  modern 
times,  the  ovolo  has  been  introduced  in  many  instances,  which  is 
preferred  on  account  of  its  superior  strength,  and  the  beautiful 
variety  of  light  and  shade  which  it  presents  to  the  eye.  "We  find 
some  examples  overcharged  with  mouldings,  which  are  not  only 
offensive  to  the  eye,  but  destroy  the  appearance  of  strength  and 
proportion.  An  error  of  this  kind  is  found  in  the  Diocletian  Baths, 
in  which  the  graceful  simplicity  is  lost,  when  compared  with  the 
Grecian  Temple  of  Theseus.  In  the  cornice,  the  facia  has  too 
much  projection,  and  is  not  deep  enough,  and  would  have  a  far 
better  appearance  were  the  dentils  quarter  round,  and  bead  left 
out.  They  are  not  considered  as  properly  belonging  to  the  Doric 
order.  Palladio  and  others  (as  shown  in  some  of  the  Roman  ex- 
amples given  in  this  work)  made  use  of  a  plain,  simple  bed  mould, 
composed  of  a  hollow  and  round,  under  the  planceer.  This  is  as 
much  as  belongs  to  the  Doric. 

In  the  Ionic,  the  Greeks  have  made  xise  of  the  eclunus,  dentils, 
an  angular  fillet,  and  a  quarter  round,  under  the  planceer,  as  in  the 
example  from  the  Temple  of  Minerva  Polias.  The  extraordinary 
projection  of  the  dentils,  rising  above  a  plain  frieze,  has  a  beautiful 
effect,  as  well  as  the  modillions  in  the  Corinthian  order.  This  mo- 
dilUon  is  frequently  ornamented  with  foliage  ;  a  decoration  properly 
belonging  to,  and  supporting,  the  planceer.  The  ornamented  ovolo 
under  the  modillions,  as  found  in  the  portico  of  the  Pantheon,  by 
its  chaste  appearance,  occasioned  by  not  adding  a  sui'plus  of  variety, 
is  rendered  one  of  the  best  specimens  of  the  Romans.  The  example 
taken  from  the  Temple  of  Jupiter  Stator  is  very  beautiful.  The 
majestic  proportions  of  the  capital  and  entablatui'o  would  give  it 
the  superiority,  were  it  not  overcharged  with  too  much  finery.  The 
addition  of  dentils,  however,  can  be  no  objection  to  its  pleasing 
effect,  as,  in  cities,  eave  cornices  are  not  often  viewed  to  advantage 
at  a  greater  distance  than  the  angle  of  forty-five  degrees,  and  within 
that  distance  the  ornamented  planceer  shows  to  good  advantage:. 
The  proportions  of  cornices  should  invariably  be  regulated  according 
to  these  distances.  If  at  the  angle  of  forty-five  degrees,  the  height 
should  be  equal  to  its  projections.  If  short  of  tliis,  its  projections 
should  increase,  in  regular  projiortion,  in  all  its  members.  l"he 
cro«ni  moulding  of  the  cornices  should  be  projected  i^-ith  soma 
variation,  —  the  Grecian  ovolo  at  forty-five  degrees, — but  the  cima 
recta  shoiJd  not  project  so  much,  in  order  to  open  it  more  to  the 
rays  of  light  j  for  if  the  swell  does  not  receive  a  strong  light,  it  is 
rendered  obscure  at  any  considerable  height. 

I  have  introduced  in  tliis  place  several  designs  for  cornices,  which 
may  assist,  in  some  measure,  the  fancy  of  those  who  may  wish  to 
vary  from  the  original  Greek  and  Roman  styles  and  proportions. 
They  may  be  executed  on  frontispieces,  and  many  other  places, 
to   advantage. 


104 


CHIMNEY-PIECES. 


Plate  60. 

Presents  five  cornices,  with  the  scale  to  wiiich 
they  are  drawn.  The  scale  is  supposed  to  be  the 
diameter  of  the  shaft  of  the  column,  at  the  bottom  ; 
from  which  these  designs  arc  figured  in  proportional 
parts.  Figs.  1  and  5  arc  plain  plancccrs ;  3  and  4 
ornamented  friezes  and  entablatures.  No.  1,  plan  of 
the  plancccr  of  Figs.  3  and  4. 

Plate  61. 

Fig.  1.  Design  of  a  modillion  cornice.  No.  1,  the 
modillion  and  manner  of  drawing  it,  viz. :  From  A 
radiate  from  1  to  2  ;  from  B  to  1  and  3 ;  liom  C  to 
3  and  4,  which  completes  the  lower  curve. 

Fig.  2.  A  cornice  without  the  entablature.  No.  2, 
design  of  the  planceer,  with  mutules  and  ornament. 

Fig.  3.  Design  of  a  Doric  entablature.  No.  3,  or- 
namented planceer. 

Fig.  4.  A  Doric  entablature  and  cornice.  No.  4, 
mutules  with  a  reset. 


CHIMNEY-PIECES. 

It  is  a  remarkable  fact  that  neither  the  Italian  nor  the  French, 
nor  indeed  any  of  the  continental  nations,  hare  over  excelled  in  com- 
positions of  chimney-pieces.  It  is  believed  that  Inigo  Jones,  em- 
inently distinguished  among  the  arcliitects  of  England,  ■was  the 
first  who  arrived  at  any  great  degree  of  perfection  in  this  important 
branch  of  architectural  science.  Other  architects  have,  smco  his 
time,  wrought  upon  his  ideas,  or  furaishcd  good  inventions  of  their 
own  ;  and  of  our  many  ingcnions  and  very  able  artists,  -whoso  prov- 
ince it  is  to  execute  magnificent  chimney-pieces  in  marble,  happily 
much  in  vogue,  it  may  be  said  that,  for  taste  of  design  and  excel- 
lence of  workmanship,  they  are  not  surpassed  by  those  of  any  other 
nation.  It  was  facetiously  observed  by  Sir  W'illiam  Chambers,  that 
chimney-pieces  should  be  "  so  situated  as  to  be  immediately  seen  by 
those  who  enter,  that  they  may  not  have  the  persons  already  in  the 
room,  who  are  generally  seated  about  the  fire,  to  search  for."  There 
is  much  good  sense  in  this  remark. 


As  the  Egyptians,  the  Greeks,  and  the  Romans, 
to  whom  architecture  is  so  much  indebted  in  other 
respects,  lived  in  warm  climates,  where  fires  in  the 
apartments  were  seldom  or  never  necessary,  they 
have  thrown  but  little  light  on  this  branch  of  archi- 
tecture. Amongst  the  antiquities  of  Italy,  I  do  not 
recollect  any  remains  of  chimney-pieces.  Palladio, 
indeed,  mentions  two  —  the  one  at  Baia,  and  tlie 
other  near  Civita  Vecchia,  which  stood  in  the  mid- 
dle of  the  room,  and  consisted  of  columns  support- 
ing architraves,  whereon  were  placed  the  pyramids 
or  funnels  through  which  the  smoke  was  conveyed. 


Scamozzi  takes  notice  of  three  sorts  of  chimney- 
pieces  used  in  Italy  at  his  time.  One  of  these  he 
calls  the  Roman,  the  apcrtiure  of  which  is  surrounded 
only  with  a  clumsy  architrave ;  another  he  calls 
Venetian,  which  is  likewise  adorned  with  an  archi- 
trave, upon  which  arc  placed  a  frieze  and  cornice, 
and  on  the  sides  thereof  are  pilasters  with  consoles. 
The  third  sort  he  calls  a  Padiglione. 

This  last  he  particularly  recommends  where  the 
walls  are  thin,  if  not  being  hollowed  into  the  wall, 
as  both  the  other  sorts  arc,  but  composed  of  a  pro- 
jecting entablatm'c  supported  by  consoles,  termini,  or 
caryatides,  on  which  the  pyramid  is  placed.  This 
sort  of  chimney-piece  is  still  very  common  in  Italy. 
The  Dutch  are  very  fond  of  it,  and  it  may  be  found 
in  many  old  English  country-houses. 

The  size  of  the  chimney-piece  must  depend  upon 
the  dimensions  of  the  room  wherein  it  is  placed.  Li 
the  smallest  apartments,  the  width  of  the  aperture  is 
never  made  less  than  from  three  feet  to  three  feet  six 
inches  ;  in  rooms  from  twenty  to  twenty-four  feet 
square,  or  of  equal  superficial  dimensions,  it  may  be 
four  feet  wide  ;  in  those  of  twenty-five  to  thkty, 
from  four  to  four  and  a  half;  and  in  such  as  exceed 
these  dimensions,  the  aperture  may  be  extended  to 
five,  or  five  feet  sbc  inches  ;  but  should  the  room  be 
extremely  large,  as  is  frequently  the  case  with  halls, 
galleries,  and  saloons,  and  one  chimney  of  these 
last  dimensions  neither  afford  sufficient  heat  to  warm 
the  room,  nor  sufficient  space  round  it  for  the  com- 
pany, it  will  be  much  more  convenient,  and  far  hand- 
somer, to  have  two  chimncy-piec"cs  of  a  moderate 
size,  than  a  single  one  exceedingly  large,  all  the  parts 
of  which  would  appear  clumsy  and  disproportioncd 
to  the  other  decorations  of  the  room.  The  chimney 
should  always  be  "  so  situated  as  to  be  immediately 
seen  by  those  who  enter,  that  they  may  not  have  the 
persons  already  in  the  room,  who  arc  generally 
seated  about  the  fire,  to  search  for."  The  middle  of 
the  side  partition  wall  is  the  most  proper  place  in 
halls  and  saloons,  and  Ihe  other  rooms  of  passage  to 
which  the  principal  enlranccs  are  commonly  in  the 
middle  of  the  front,  or  of  the  back  wall ;  but  in 
drawing-rooms,  dressing-rooms,  and  the  like,  the 
middle  of  the  back  wall  is  the  best  situation,  the 
chimney  being  then  farthest  removed  from  the  doors 
of  communication.  Tlie  case  is  the  same  with  re- 
spect to  galleries  and  libraries,  whose  doors  of  en- 
trance are  generally  cither  at  one  or  both  ends.     In 


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105 


bed-chambers  the  chimney  is  always  placed  in  the 
middle  of  one  of  the  side  partition  walls,  and  in 
closets,  or  other  very  small  places.  It  is,  to  save 
room,  sometimes  placed  in  one  corner. 

Whenever  two  chimney?  are  introduced  in  tlie 
same  room,  they  must  be  regularly  placed,  either 
directly  facing  each  other,  if  in  different  walls,  or  at 
equal  distances  from  the  centre  of  the  wall  in  which 
they  are  both  placed.  The  Italians  frequently  put 
their  chimneys  in  the  front  walls  between  the  win- 
dows, for  the  benefit  of  looking  out  while  sitting  by 
the  fire. 

The  proportion  of  the  apertures  of  chimney-pieces 
of  a  moderate  size  is  generally  near  a  square ;  in 
small  ones,  a  trifle  higher ;  and  in  larger  ones,  some- 
what lower.  Chimney-pieces  are  made  either  of 
stone  or  marble,  or  of  a  mixture  of  these  with  wood, 
scagUola,  or  molu,  or  some  other  unfragile  substances. 
Those  of  marble  are  most  costly,  but  they  are  also 
most  elegant,  and  the  only  ones  used  in  high-finished 
apartments,  where  they  are  seen  either  of  white  or 
variegated  marbles,  sometimes  iidaid  and  decorated 
with  the  materials  just  mentioned.  All  their  orna- 
ments, figures,  or  profiles  are  to  be  made  of  the  pure 
white  sort ;  but  their  friezes,  tablets,  panels,  shafts 
of  columns,  and  other  plain  parts,  may  be  of  party- 
colored  marbles,  such  as  the  yellow  of  Sienna,  the 
brocatello  of  Spain,  the  jaspers  of  Sicily,  and  many 
other  modern  as  well  as  antique  marbles  firequently 
to  be  had  in  this  country.  Festoons  of  flowers, 
trophies,  and  foliages,  frets,  and  other  such  decora- 
tions cut  in  white  statuary  marble,  and  fixed  on 
grounds  of  these,  have  a  very  good  effect.  But  there 
should  never  be  above  two,  or  at  the  utmost  three, 
different  sorts  of  colors  in  the  same  chimney-piece, 
all  brilliant  and  harmonizing  with  each  other.  In 
the  inferior  class  of  houses,  and  in  upper  chambers, 
wood  is  generally  used  in  the  construction  of  chim- 
ney-pieces, painted  and  varnished  so  as  to  resemble 
marble.  The  use  of  wooden  chimney-pieces,  when 
judiciously  applied,  materially  lessens  the  expense, 
and  answers  every  purpose  of  utility  or  ornament. 

In  many  places,  the  wildest  notions  have  been  in- 
dulged in  the  designs  of  this  part  of  architecture. 
Sometimes  we  see  a  chimney-piece,  the  shelf  of  which 
is  supported  on  a  numerous  variety  of  mouldings,  piled 
one  above  the  other  until  they  project  nearly  as  much 
as  the  shelf  itself;  this,  I  contend,  is  useless  and  out  of 
,  good  taste,  for  they  cannot  be  seen  to  any  advantage, 

14 


as  in  ordinary  eases  they  fall  below  the  eye,  except 
when  seated,  and  then  they  are  so  nearly  on  a  level 
with  it  that  they  cannot  be  seen  to  any  advantage. 
If,  therefore,  one  half  of  the  expense  of  mouldings 
should  be  laid  out  in  the  frieze  and  pilasters,  or  col- 
umns, they  would  have  a  much  better  appearance, 
and  display  a  more  refined  taste. 

Plate   62. 

On  tills  plate  will  be  found  two  designs  for  com- 
mon chimney-pieces,  drawn  to  a  scale  of  feet  and 
inches. 

Plate   63. 

On  this  plate  will  be  found  two  designs  for  chim- 
ney-pieces, as  executed  by  Isaiah  Rogers,  Esq.,  in  the 
Tremont  House,  Boston,  Massachusetts,  drawn  firom 
the  same  scale  as  plate  62. 


DOORS. 

In  our  northern  climate,  the  fewer  doors  a  room  has  the  more  it 
■will  be  comfortably  habitable  ;  for  as  vre  have  much  more  cold  than 
hot  weather,  it  is  yery  necessary  to  make  the  rooms  as  close  as  pos- 
sible, otherwise  they  will  not  be  fit  to  live  in  the  greater  part  of  the 
year.  Wherefore  it  will  be  advisable  never  to  make  either  more 
windows  or  doors  than  are  absolutely  necessary.  In  this  country, 
the  real  and  feigned  doors  of  a  room,  with  their  ornaments,  fre- 
quently cover  so  great  a  part  of  the  walls  that  there  is  no  place 
left  for  either  pictures  or  furniture. 


Doors  of  entrance  to  private  houses  should  not  be 
less  than  three  feet  wide,  nor  more  than  six  feet ;  but 
to  churches,  theatres,  and  other  public  structures, 
where  there  is  a  constant  ingress  and  egress  of  peo- 
ple, and  firequently  great  crowds,  the  apertures  must 
be  larger,  and  their  width  cannot  be  less  than  six  feet, 
nor  should  it  exceed  ten  or  twelve. 

Li  settling  the  dimensions  of  the  apertures  of  doors, 
regard  must  be  had  to  the  architecture  with  which 
the  door  is  surrounded.  K  it  be  placed  in  the  inter- 
columniation  of  an  order,  the  height  of  the  aperture 
should  never  exceed  three  quarters  of  the  space  be- 
tween the  pavement  and  the  architrave  of  the  order, 
otherwise  there  cannot  be  room  for  the  ornaments  of 
the  door.  Nor  should  it  ever  be  much  less  than  two 
thirds  of  that  space,  for  then  there  will  be  room  suf- 
ficient to  introduce  both  an  entablature  and  a  pedi- 
ment without  crowding;  whereas,  if  it  be  less,  it  will 
appear  trifling,  and  the  intercolumniation  will  not  be 
sufficiently  filled.  The  apertures  of  doors  placed  in 
arches  are  regulated  by  the  imposts,  the  top  of  the 


106 


DOORS. 


cornice  being  generally  made  level  with  the  top  of 
the  impost.  And  when  doors  are  placed  in  the  same 
line  with  windows,  the  top  of  the  aperture  should 
level  with  the  tops  of  the  apertures  of  the  windows ; 
or  if  that  be  not  practicable  without  making  the  door 
much  larger  than  is  necessary,  the  aperture  may  be 
lower  than  those  of  the  windows,  and  the  tops  of  all 
the  cornices  made  on  the  same  level. 

With  regard  to  the  situation  of  the  principal  en- 
trance, Palladio  observes,  that  it  should  be  so  placed 
as  to  admit  of  an  easy  communication  with  every 
part  of  the  buUding.  Scamozzi  compares  it  to  the 
mouth  of  an  animal;  and  as  nature,  says  he,  has 
placed  the  one  in  the  middle  of  the  face,  so  the  archi- 
tect ought  to  place  the  other  in  the  middle  of  the 
front  of  the  edifice,  that  being  the  most  noble  situa- 
tion, the  most  majestic  and  convenient.  In  several 
of  the  palaces  at  Rome,  as  those  of  the  Pamfili  in 
the  Corso,  and  of  the  Bracciano,  at  Santi  Apostoli, 
there  are  two  principal  entrances  in  the  same  aspect ; 
but  this  is,  in  general,  to  be  avoided,  as  it  leaves 
strangers  in  doubt  where  to  seek  for  the  state  apart- 
ments, which  should  always  be  contiguous  to  the 
principal  entrance.  In  interior  dispositions,  the  doors 
of  communication  must  be  situated,  as  much  as  pos- 
sible, in  a  line ;  the  advantages  of  which  are,  that  it 
contributes  towards  the  regularity  of  the  decoration, 
and  facilitates  and  shortens  the  passage  through  the 
apartments  in  summer ;  or  on  public  occasions,  when 
the  doors  are  set  open,  it  produces  a  free  circulation  of 
air,  and  likewise  gives  a  much  more  splendid  appear- 
ance to  the  apartments,  by  exposing  to  view  at  once 
the  whole  series  of  rooms,  which  is  more  particularly 
striking  when  the  apartments  are  illuminated,  as  on 
occasions  of  balls,  routs,  or  other  rejoicings.  There 
should,  if  possible,  be  a  window  at  each  end  of  the 
building,  directly  facing  the  line  of  the  doors  of  com- 
munication, so  that  the  view  may  be  more  extensive, 
and  take  in  at  once  not  only  all  the  rooms,  but  like- 
wise parts  of  the  gardens,  or  other  prospects  sur- 
rounding the  building ;  and  whenever  this  is  not 
practicable,  it  will  do  well  to  place  mirrors  at  each 
end  of  the  apartment,  or  to  counterfeit  doors,  and  fill 
them  with  large  plates  of  glass,  or  with  sashes  and 
squares  of  looking-glass,  as  is  the  custom  in  France, 
which  by  reflection  mu'tiply  the  rooms,  the  doors, 
and  other  objects,  making  an  apartment,  though  lim- 
ited or  small,  appear  very  considerable. 

The  door  of  entrance  from  halls,  vestibules,  or  ante- 


chambers, either  to  the  principal  apartment  or  to  any 
even  of  the  inferior  ones,  should  be  in  the  middle 
of  the  room,  if  possible,  and  facing  a  window ;  those 
that  lead  to  galleries,  or  any  other  long  rooms,  should 
be  in  the  middle  of  one  of  the  ends ;  and  in  general, 
all  entrances  should  be  so  contrived  as  to  offer  to 
view,  at  the  first  glance,  the  most  magnificent  and 
extensive  prospect  of  the  place  they  open  into.  The 
doors  of  communication  from  one  room  to  another 
of  the  same  apartment  must  be  at  least  two  feet  dis- 
tant from  the  front  walls,  that  the  tables  placed  against 
the  piers,  between  the  windows,  or  other  pieces  of 
furniture  put  there,  may  not  stand  in  the  way  of 
those  who  pass.  In  bed-rooms,  care  must  be  taken 
to  make  no  doors  on  the  sides  of  the  bed,  unless  it 
be  to  communicate  with  a  water  closet,  wardrobe, 
bath,  or  other  eonveniency  of  that  kind,  as  well  on 
account  of  t"he  draught  of  air  as  of  the  noise  commu- 
nicated through  them,  or  attending  their  opening  and 
shutting;  both  of  which  are  always  troublesome,  and 
on  some  occasions  dangerous.  Neither  ought  doors 
to  be  placed  near  chimneys,  for  the  same  reasons, 
and  as  the  opening  of  them  would  disturb  those  who 
sit  by  the  fire. 

In  composing  doors,  regard  must  be  had,  both  in 
their  size  and  enrichments,  to  the  place  they  lead  to. 
Those  that  give  entrance  to  churches,  theatres,  state 
apartments,  or  other  places  of  consequence  must  be 
large  and  profusely  enriched ;  but  such  as  open  to 
humbler  habitations  may  be  small  and  sparingly 
decorated,  unless  the  nature  of  the  building  should 
require  otherwise.  Where  several  doors  are  in  the 
same  aspect,  as  on  the  inside  of  a  hall,  saloon,  or  gal- 
lery, they  should  be  all  of  the  same  size  and  figure, 
unless  there  be  many,  in  which  case  the  principal 
ones,  provided  they  stand  in  the  middle  of  a  side,  or 
in  the  middle  of  the  ends  of  the  room,  may  be  larger, 
of  a  different  form,  and  more  abundantly  adorned 
than  the  rest.  But,  whenever  more  than  two  sorts 
are  introduced  in  one  room,  it  always  tends  to  con- 
fuse the  spectator. 

The  commonest  sort  of  doors  are  made  of  pine, 
painted  in  various  manners,  and  the  better  kind  of 
them  are  of  mahogany,  or  oak,  or  different  sorts  of 
rare  wood,  inlaid.  With  regard  to  their  construction, 
strength,  beauty,  and  straightness  are  to  be  consid- 
ered ;  all  which  purposes  are  answered  by  composing 
them  of  several  panels.  The  number  of  these  must 
depend  on  the  size  of  the  door,  which  should  like- 


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Fif,.  t. 


WINDOWS. 


107 


wise  regtilate  the  thickness  both  of  the  panels  and 
the  framing.  If  the  doors  be  adorned  with  orna- 
ments of  sculpture,  as  is  sometimes  usual  in  very  rich 
buildings,  they  must  either  be  sunk  in,  or  kept  very 
flat  upon,  the  sm-face,  both  for  tlic  sake  of  lightness, 
and  to  prevent  their  being  broken.  The  panels  may 
be  either  raised  or  flat,  and  surrounded  with  one  or 
two  little  plain  or  enriched  mouldings,  contained  in 
the  thickness  of  the  framing,  not  projecting  beyond 
it,  as  is  sometimes  seen  in  old  buildings. 

Doors  that  exceed  three  feet  and  a  half  in  breadth 
are  generally  composed  of  two  flaps,  by  which  means 
each  part  is  lighter ;  when  open,  does  not  project  so 
far  into  the  room ;  and  when  required,  may  be  made 
to  fold  entirely  into  the  thickness  of  the  wall.  It  is 
to  be  observed,  that  all  doors  should  open  inwards ; 
otherwise,  in  opening  a  door  to  give  a  person  en- 
trance, it  must  open  in  his  face,  and  may  chance  to 
knock  him  down. 

For  a  variety  of  doors,  in  the  modern  taste,  see 

plates  64,  65,  66. 

Plate  64. 

On  plate  64  will  be  found  sLs  designs  for  inside 
doors,  with  the  finish.  The  proportions  of  each  part 
are  figured,  and  across  each  will  be  seen  a  sectional 
plan,  showing  panels,  &c.,  either  raised  or  sunken, 
as  the  case  may  be.  A  is  an  elevation  of  a  circular 
head  door,  and  is  designed  for  an  outside  door.  The 
architraves  of  each  at  1,  2,  and  3,  are  those  on 
plate  30.  —  Editors. 

Plate  65. 

Figs.  1  and  2.   Designs  for  outside  doors. 

Figs.  3  and  4.  Horizontal  section  of  the  same,  with 
a  projection  of  the  threshold,  steps,  and  pilasters. 

Fig.  5.    Section  of  the  style,  panel,  and  moulding. 

Fig.  6.    Section  of  the  pilaster  and  plinth. 

Plate  66. 

Fig.  1.  Front  door  finished  in  the  Ionic  style,  the 
pillars  supporting  the  cap  in  the  wall. 

Fig.  2.    The  recess  and  side  view  of  the  column. 

Fig.  3.  The  recess  of  the  door  from  the  column 
and  step  on  which  the  pillars  stand. 

Fig.  4.  The  ceiling  of  the  recess  and  inverted  cap- 
itals of  the  column. 

Fig.  5.    Style,  panel,  and  moulding  of  the  door. 

Good  taste  has  taught  us  to  avoid  the  multiplica- 
tion of  small  members  on  inside  finishing,  and  to 
adopt  in  their  place  plane  surfaces,  or  appropriate 


mouldings  of  a  proper  size  with  their  necessary  ar- 
rangements, as  it  is  much  easier  executing  a  proper 
finish  of  painting :  the  necessary  application  of  a 
pumice  stone  or  sand  paper,  to  produce  a  smooth 
surface,  is  rendered  impracticable,  by  numerous  close 
quirks,  without  injuring  the  paint  on  the  otJHT  parts. 
On  a  plane  surface,  the  work  is  much  easier  cleansed ; 
and  by  this  style  of  finish,  which  rejects  every  thing 
that  is  mean  and  trifling,  that  manly  character  is 
given  to  the  work  which  the  refined  taste  of  ancient 
and  modern  architects  have  so  much  admired. 

The  Proportions  of  the  Architraves  and  Pilasters  for 
inside  Finish. 

The  architraves  for  windows  and  doors  in  any  one 
apartment  should  be  nearly  of  the  same  width,  where 
a  uniformity  of  appearance  requires  it.  Add  together 
the  width  of  the  door  and  of  the  window  and  the 
splay ;  find  the  mean  width ;  then  divide  it  by  7,  which 
gives  the  width  of  the  architrave  ;  but  where  fancy 
pilasters  are  required,  divide  by  6,  which  gives  one 
sixth  of  the  width  of  the  opening  for  the  width  of  the 
pilasters.  The  designs  in  plate  30  give  the  full  size 
that  those  in  general  use  are  executed. 


CONSTRUCTION    OF    WINDOWS. 

There  has  been  in  this  branch  of  architecture,  as  well  as  all  oth- 
ers, a  variety  of  changes  and  modifications  to  suit  the  taste  and 
fashion  of  the  times.  In  civilized  countries,  convenience  and  beauty 
are  consulted  ;  whereas,  in  barbarous  countries,  strength  and  safety 
are  their  most  necessary  requisites.  In  this  enlightened  and  happy 
country,  every  man  of  taste  adorns  his  habitation  with  such  as  he 
may  deem  to  be  most  convenient,  economical,  and  ornamental.  The 
enriching  of  windows  with  ornaments  is  of  ancient  date,  and  has 
been  handed  down  to  us  in  common  with  most  of  the  grand  princi- 
ples of  the  arts  and  sciences. 


The  proportions  of  the  apertures  of  windows  de- 
pend upon  their  situation ;  their  width  in  all  the 
stories  must  be  the  same,  but  the  different  heights  of 
the  apartments  make  it  necessary  to  vary  the  heights 
of  the  windows  likewise.  In  the  principal  floor  it 
may  be  from  two  and  one  eighth  of  the  width  to  two 
and  one  third,  according  as  the  rooms  have  more  or 
less  elevation ;  but  in  the  ground  floor,  where  the 
apartments  are  usually  somewhat  lower,  the  aper- 


108 


WINDOWS. 


tures  of  the  windows  should  seldom  exceed  a  double 
square ;  and  when  they  are  in  a  rustic  basement,  they 
are  frequently  made  much  lower.  The  windows  of 
the  second  floor  may  be,  in  height,  from  one  and  a 
half  of  their  width  to  one  and  four  fifths ;  and  those 
of  attics  or  mezzanines,  either  a  perfect  square  or 
somewhat  lower.  The  character  of  the  order  in 
which  the  windows  are  employed,  and  that  of  the 
profiles  with  which  they  are  enriched,  must  likewise, 
in  some  measure,  be  consulted,  and  the  apertures  be 
made  more  or  less  elevated,  as  the  order  of  the  whole 
decoration,  or  of  the  window  itself,  is  more  or  less 
delicate. 

The  windows  of  the  principal  floor  are  generally 
most  enriched.  The  simplest  method  of  adorning 
them  is  with  an  architrave  surrounding  the  aperture, 
covered  with  a  frieze,  and  cornice  suited  thereto ;  but 
when  the  aperture  is  remarkably  high  with  respect  to 
its  width,  it  becomes  necessary  to  spread  the  orna- 
ments on  the  sides  thereof,  by  flanking  the  architrave 
with  columns,  pUasters,  or  consoles,  in  order  to  give 
the  whole  composition  an  agreeable  proportion. 
The  windows  of  the  ground  floor  are  sometimes 
left  entirely  plain,  without  any  ornaments  whatever ; 
at  other  times,  they  are  surrounded  with  an  archi- 
trave, or  with  rustics,  or  have  a  regular  architrave 
crowned  with  its  frieze  and  cornice.  Those  of  the 
second  floor  have  generally  an  architrave  carried 
entirely  round  the  aperture;  and  the  same  is  the 
method  of  adorning  attic  or  mezzanine  windows. 
But  these  two  last  have  seldom  or  ever  either  frieze 
or  cornice  ;  whereas,  the  second  floor  windows,  when- 
ever their  aperture  approaches  a  double  square,  are 
often  adorned  with  both. 

The  sills  of  the  windows  on  the  same  floor  should 
be  on  the  same  level,  and  raised  above  the  floor  from 
two  feet  nine  inches  to  three  feet  at  the  very  most. 
When  the  walls  are  thick,  they  should  be  reduced 
under  the  aperture  of  the  windows,  for  the  conven- 
iency  of  looking  out,  and  seats  may  be  contrived  to 
fit  these  recesses,  as  is  the  custom  in  many  modern 
houses.  In  France,  and  now  too  often  here,  the  win- 
dows are  carried  quite  down  to  the  floor,  which,  when 
the  building  is  surrounded  with  gardens  or  other  beau- 
tiful prospects,  renders  the  apartments  exceedingly 
pleasant  in  summer,  but  then  they  become  exceed- 
ingly cold  in  winter ;  and  the  iron  work,  which  in 
France,  and  latterly  very  nmch  here,  is  placed  on  the 
outside  by  way  of  fence  against  accidents,  ought 


never  to  take  place  where  regular  architecture  is 
intended ;  for  all  the  gilding  and  flourishing  in  the 
world  can  never  make  it  tolerably  accordant  with  the 
rest  of  the  composition. 

In  regular  built  houses,  the  sills  of  the  windows 
on  the  ground  floor  should  be  raised  six  feet  above 
the  pavement  on  the  outside  of  the  building,  to  hin- 
der passengers  from  looking  into  the  apartments ; 
but  when  this  cannot  be  done  without  raising  the 
floor  itself  more  than  may  be  necessary,  the  lower 
parts  of  the  windows  may  be  furnished  with  blinds. 
The  tops  of  the  apertures  of  windows  should  never, 
within  the  apartments,  be  carried  up  close  to  the  cor- 
nice of  the  room.  A  sufficient  space  ought  always 
to  be  left  for  an  architrave,  or  at  least  two  or  three 
inches  between  the  architrave  and  cornice  —  a  space 
usually  occupied  by  the  cvirtain  lath. 

The  interval  between  the  apertures  of  windows 
depends,  in  a  great  measure,  on  their  enrichments. 
The  width  of  the  aperture  is  the  smallest  distance 
that  can  be  between  them,  and  twice  that  width 
should,  in  dwelling-houses,  be  the  largest ;  otherwise, 
the  rooms  will  not  be  sufficiently  lighted,  and  the 
building  will  have  rather  the  appearance  of  a  prison 
than  of  a  structure  calculated  for  the  conveniences 
and  enjoyments  of  life.  The  purpose  for  which  the 
building  is  intended  should  regulate  the  quantity  of 
light  to  be  introduced ;  and,  therefore,  in  dwelling- 
houses,  and  all  places  where  comfort  and  pleasure 
arc  the  main  purposes,  there  cannot  be  too  much. 
But  in  sacred  structures,  which  should  affect  the 
mind  with. awe  and  with  reverence,  or  in  other  great 
works  where  grandeur  of  style  is  aimed  at,  it  should 
be  cautiously  and  rather  sparingly  distributed. 

The  windows  nearest  to  the  outward  angles  must 
be  at  least  the  width  of  their  aperture  distant  from 
the  angle,  and  a  larger  space  will  be  still  more  seemly, 
and  render  the  building  more  solid.  In  all  the  stories 
of  the  same  aspect,  the  windows  must  be  placed 
exactly  one  above  the  other,  and  those  to  the  left 
symmetrize  with  those  to  the  right,  in  size,  situation, 
number,  and  figure. 

The  reasons  for  all  these  things  are  obvious  enough, 
and,  therefore,  it  is  needless  to  mention  them.  The 
licentious  practice  of  intermitting  the  architrave  and 
frieze  of  an  order  in  the  intervals  between  the  col- 
umns or  pilasters,  to  make  room  for  windows  and 
their  enrichments,  which  are  carried  close  up  to  the 
cornice,  can  on  no  account  whatever  be   suffered  in 


WINDOWS. 


109 


regular  architecture,  it  being  in  the  highest  degree 
absurd  to  carry  the  windows  above  the  ceiling,  and 
great  want  of  judgment  in  an  architect  to  intermix 
and  crowd  together  such  a  number  of  rich  complicat- 
ed parts  as  are  those  of  the  entablature  of  the  order 
and  the  entablatures  of  the  windows.  Besides,  the 
whole  beauty  of  the  order,  when  so  mutilated,  is 
destroyed,  its  proportions  and  figure  being  entirely 
changed.  An  interruption  of  the  whole  entablature 
to  make  room  for  a  window,  and  converting  it  into 
an  impost  to  the  architrave,  is  a  license  equally  un- 
pardonable. 

The  common  sort  of  builders  in  this  country  are 
extremely  fond  of  variety  in  the  ornaments  of  win- 
dows, and,  indeed,  in  every  other  part  of  a  building, 
imagining,  probably,  that  it  betrays  a  barrenness  of 
invention  to  repeat  the  same  object  frequently.  I 
have  seen  a  house  with  only  eleven  windows  in  the 
whole  front,  and  yet  there  were  seven  different  sorts. 
At  another  place,  the  case  is  the  same,  there  being 
seven  or  eight  sorts  of  windows  in  the  same  aspect ; 
and  the  like  is  to  be  met  with  in  many  other  build- 
ings, both  in  town  and  in  the  country.  These  in- 
ventive gentlemen  would  do  well  to  give  their  atten- 
tion to  some  professors  of  the  mechanic  arts,  who, 
though  exercising  their  talents  on  meaner  objects,  are 
nevertheless  worthy  of  their  imitation.  No  taUor 
thinks  of  employing  seven  or  eight  kinds  of  buttons 
on  the  same  coat ;  a  cutler  will  not  make  ten  dif- 
ferent sorts  of  knives  for  the  same  set;  and  if  a 
cabinet  maker  be  trusted  to  furnish  a  room,  he  sel- 
dom introduces  more  than  one  or  two  sorts  of 
chairs :  their  practice  is  founded  on  experience ;  the 
general  approbation  of  mankind  is  the  standard  they 
go  by. 

We  do  not  discover,  either  in  the  works  of  an- 
tiquity or  those  of  the  great  modern  architects,  any 
traces  of  this  childish  hankering  after  variety.  The 
same  object  is  frequently  by  them  repeated  a  hun- 
dred times  over ;  and  this  is  one  of  the  causes  of  that 
amazing  grandeur,  that  noble  simplicity,  so  much  to 
be  admired  in  their  productions. 

This  sameness  must,  however,  have  its  limits ;  for, 
when  carried  too  far,  the  imagination  of  the  beholder 
stagnates  for  want  of  occupation.  In  the  most  ad- 
mired marks  of  architecture,  we  find  the  same  objects 
generally  continued  throughout  the  same  level :  thus 
one  order  and  one  sort  of  windows  or  niches  gener- 
ally reign  throughout  the  story  ;  but  in  other  stories. 


where  the  eye  and  the  imagination  necessarily  as- 
sume a  fresh  course,  the  decoration  is  altered. 

Sometimes,  however,  it  may  be  necessary  to  in- 
crease the  size,  and  vary  the  figures,  of  the  windows, 
either  in  the  centre  break  or  in  some  other  prominent 
part  of  a  front,  in  order  to  light  a  saloon,  a  gallery,  or 
a  hall  higher  than  the  rest  of  the  room.  But  then  it 
will  always  be  advisable  to  repeat  the  same  form  if 
simple,  as  an  arch,  three,  five,  or  more  times,  accord- 
ing to  the  extent  of  the  plan,  so  that  the  mind  may 
be  in  some  degree  satiated  before  it  is  conducted  to 
a  new  object. 

Venetian  windows  and  Venetian  doors,  too,  are 
on  some  occasions  necessary,  particularly  in  small 
buildings,  to  light  a  hall,  a  vestibule,  or  such  other 
rooms  as  cannot  admit  of  two  windows,  and  yet 
would  not  be  sufficiently  lighted  with  one.  But 
where  they  can  be  avoided,  it  is  best ;  for  the  col- 
umns which  separate  the  large  interval  from  those 
on  the  sides  form  such  slender  partitions,  that,  at  a 
distance,  they  are  scarcely  perceived,  and  the  whole 
looks  like  a  large,  irregular  breach  made  in  the 
wall ;  and,  however  advisable  it  may  be  to  repeat  the 
same  form  as  has  above  been  mentioned,  the  repeti- 
tion of  these  Venetian  windows  should  always  be 
avoided. 

The  sashes  of  windows  are  generally  made  of  pine, 
cherry,  or  mahogany,  and  sometimes  of  iron,  copper, 
or  other  metals.  Our  artificers  excel  in  these  works ; 
they  make  them  very  neatly,  and  though  in  appear- 
ance slight,  very  strong.  The  lights  of  glass  are 
proportioned  to  the  size  of  the  windows,  there  being 
commonly  three  in  width  and  four  in  height,  what- 
ever be  the  dimensions  of  the  window ;  each  sash  is 
composed  of  two  equal  parts,  placed  one  above  the 
other,  and  either  the  lowermost,  or  both  of  them, 
being  hung  on  pulleys  and  counterpoised  with  weights, 
and  moved  up  and  down  with  great  ease,  the 
weights  being  concealed. 

The  shutters  are  always  within  the  apartments 
wherever  beauty  is  aimed  at,  those  on  the  outside 
destroying  the  appearance  of  the  front.  They  are 
divided  into  several  vertical  slips,  folding  behind 
each  other,  for  the  conveniency  of  ranging  or  boxing 
them,  when  open,  in  the  thickness  of  the  wall.  Each 
slip  or  fold  is  framed  and  composed  of  several  pan- 
els, either  raised  or  flat,  surrounded  with  small 
mouldings  contained  in  the  thickness  of  the  fram- 
ing, which,  when  the  profiles  in  the  room  are  en 


110 


WINDOWS. 


riched,  should  likewise  be  so,  at  least  on  the  fold  that 
faces  the  aperture,  when  the  shutters  are  turned 
back ;  the  front  of  which  must  stand  flush  with  the 
inner  edge  of  the  architrave  surrounding  the  window, 
all  the  other  folds  being  ranged  behind  it.  I  have 
given,  in  plate  67,  the  mode  of  finishing  window 
frames,  sashes,  and  shutters. 

Plate   67. 

Fig-.  1  shows  the  disposition  of  the  members  of  a 
windoio  frame  and  shutters. 

No.  1.  The  outside  moulding  against  the  wall. 

No.  2.  The  outside  casing. 

No.  3.  The  pulley  style. 

No.  4.  The  inside  casing. 

No.  5.  The  back  casing. 

No.  6.  The  parting  slip.  •,,    . 

No.  7.  The  parting  bead. 

No.  8,  8.  The  weights. 

No.  9.  The  recess  of  the  wall. 

No.  10,  10,  10, 10.  The  styles  of  the  shutters. 

No.  11,  11.  The  panels  of  the  shutters. 

No.  12.  The  back  furring  for  the  splay  of  the 
window. 

No.  13.  The  ground. 

No.  14.  Section  of  the  pilaster. 

No.  15.  The  back  Uning. 

No.  16.  The  thickness  of  the  plastering. 

Fig-.  2  shows  the  disposition  of  shutters  folding- 
back  on  a  right  line  toith  the  plastering. 
No.  1.  The  inside  casing. 
No.  2.  Hinge  casing. 
No.  3,  3,  3,  3.  Styles  of  the  shutters. 
No.  4,  4.  Panels. 
No.  5.  Back  casing. 

No.  6.  Box  casing.  ,  4 

No.  7.  Plastering. 
No.  8.  Band  moulding. 

Fig.  3.  Section  of  part  of  a  shutter. 
No.  1.  The  style. 
No.  2.  Panel. 
No.  3.  Moulding. 

Fig.  4.  Moulding,  different  from  Fig.  3. 

Fig.  5.  Section  through  the  frame  and  sash,  and 
shows  the  manner  of  selling  the  sash  into  the  frame. 
No.  1.  The  manner  of  joining  the  soffit  to  the  frame. 
No.  2.  Cap  of  the  frame-. 
No.  3,  3.  Casings  of  the  frame. 


No.  4.  Top  rail  of  the  sash. 

No.  5.  Munten  of  the  sash. 

No.  6,  6.  Meeting  rails. 

No.  7.  Munten. 

No.  8.  Bottom  rail. 

No.  9.  Window  sill. 

No.  10.  Stop  bead. 

No.  11.  Back. 

No.  12.  Back  bead. 

No.  13.  Outside  moulding. 

Figs.  6  and  7.   Sections  of  sash  muntens. 

Plate   68. 

On  plate  68  will  be  found  a  plan,  elevation, 
and  section  of  a  French  window,  with  the  scale  by 
which  it  was  drawn.  No.  1  shows  the  elevation ; 
No.  2,  the  plan ;  No.  3,  a  section ;  No.  4,  a  section  of 
a  part  of  the  sUl  and  the  sash ;  A  is  a  small  fillet  to 
prevent  the  water  being  driven  beneath  the  sash ;  and 
B  is  a  channel  to  receive  the  water  that  may  run 
down  on  the  outside  behind  the  fillet ;  the  dotted  line 
C  is  another  channel  at  right  angles  with  B,  to  take 
the  water  to  the  outside.  B  shows  the  manner  of 
constructing  the  meeting  styles.  The  finish  for  the 
window  may  be  either  of  the  architraves  shown  on 
plate  30 ;  and  the  manner  of  constructmg  the  shutters 
is  shown  on  plate  67. 

Plate  69. 

Plate  69  is  a  design  for  an  oriel  window.  Figure  1 
shows  the  front  elevation ;  figure  2,  the  side  elevation ; 
figure  3,  the  plan ;  and  figure  4,  the  detail  of  the  base. 
The  scale  is  placed  with  the  plan,  by  which  the  sev- 
eral parts  may  be  ascertained. 

Plate  70. 

Plate  70  *  is  a  part  of  the  details  of  plate  69.  Figs. 
1  and  2  are  the  trusses  at  D  and  A,  and  B  is  a  de- 
lineation of  the  leaf  at  C.    Fig.  3  is  a  truss  or  console. 

*  This  plate,  with  plate  69,  was  dcslgued  and  drawn  by  Mr.  Shaw, 
and  we  have  inserted  it  as  being  the  modern  production  of  one  who 
has  the  honor  of  being  among  the  earliest  of  the  American  architect- 
ural ■writers.  Mr.  Shaw's  first  edition  of  Civil  Architecture  was 
pubUshed  more  than  twenty-five  years  ago  ;  and  since  then  he  has 
contributed,  in  no  small  degree,  to  the  advancement  of  his  much- 
beloved  science,  both  practically  and  theoretically.  He  is  now  in 
the  65th  year  of  his  age ;  but,  notwithstanding  his  advancement  in 
years,  his  desire  is  as  strong  as  ever  for  the  application  of  the  correct 
principles  of  architecture  in  buildings  of  every  kind.  — Editors. 


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ELEMENTS    OF    FOLIAGE. 


Ill 


FOLIAGE. 


Both  the  elements  and  composition  of  foliage  arc  here  consid- 
ered, and  illustrated  by  plates.  The  examples  are  taken  from  the 
remains  of  the  most  esteemed  buildings  of  Grecian  and  Roman  an- 
tiquity. The  learner  is  recommended  to  go  through  all  the  variety 
of  ornaments  exhibited  in  this  department,  by  which  means  he  will 
be  enabled  to  apply  himself  to  any  other  species,  however  different. 


DEFINITIONS. 

1.  An  artificial  arrangement  or  disposition  of  leaves 
is  caMed  foliage. 

2.  The  subdivisions  of  single  leaves  are  called 
raffles.  The  leaves  which  are  chiefly  used  in  architec- 
ture are  the  acanthus,  olive,  parsley,  laurel,  and  lotus. 

3.  All  artificial  arrangement  of  leaves,  branches, 
fruit,  flowers,  drapery,  &c.,  either  singly  or  combined 
in  any  manner  with  each  other,  are  called  ornaments 
in  architecture. 

4.  A  string,  consisting  of  flowers,  imit,  leaves,  and 
branches,  either  singly  or  intermixed  with  each  other, 
and  supported  at  the  tsvo  extremes,  the  middle  part 
forming  itself  into  a  curve  by  its  gravity,  is  called  a 
festoon. 

5.  A  curve  line,  which  is  continually  changing  its 
position  in  conb-ary  directions  on  the  same  side  of  it, — 
that  is,  first  concave  and  then  convex,  concave  again 
and  then  convex  again,  and  so  on  alternately,  in  this 
manner,  to  any  number  of  curves  of  contrary  flex- 
ure, —  is  called  a  serpentine  line. 

6.  If  fi-om  a  stalk,  in  the  form  of  a  serpentine  line, 
a  number  of  branches  issue  out,  twisting  themselves 
in  the  form  of  spiral  lines,  on  each  side  of  the  ser- 
pentine, in  all  the  concave  parts  on  the  alternate 
sides  of  it,  and  if  these  spirals  and  the  stalk  be  deco- 
rated with  foUage,  —  a  composition  so  formed  is 
called  tvindiriff  foliage. 


TO     DRAW     ORNAMENTS, 


PROBLEM. 


The  learner  should,  in  the  first  place,  draw  a  great 
variety  of  curve  and  spiral  lines  of  different  descrip- 


tions, and  compare  these  figures  with  each  other,  by 
which  means  he  will  be  able  at  sight  to  distinguish 
each  particular  species  of  curve  from  another ;  then 
he  ought  to  endeavor  to  imitate,  with  precision,  the 
same  things  by  hand  in  every  variety  of  position 
which  he  can  suggest  to  himself,  and  hence  he  will 
acquire  a  freedom  of  hand  in  every  direction.  When 
he  proceeds  to  copying  leaves,  a  general  outline  ought 
to  be  drawn,  circumscribing  the  whole  leaf;  he  should 
then  form  outlines  of  aU  the  raffles,  and  round  every 
compartment,  circumscribing  all  the  different  sets  of 
points  or  raffles,  and  afterwards  proceed  to  draw  the 
raffles  themselves. 

The  learner  having  after  sufficient  practice  in  copy- 
ing acquired  a  freedom  of  hand,  he  is  advised  to 
draw  from  nature  a  variety  of  such  things  as  will  be 
most  suitable  for  the  purposes  to  which  they  are  to 
be  applied.  By  so  doing,  the  parts  of  his  composi- 
tions will  always  appear  rich  and  natural,  and  hence 
he  will  obtain  a  greater  facility  of  invention.  Hav- 
ing had  sufficient  practice  in  drawing  from  nature, 
he  may  then  apply  himself  to  the  designing  of  orna- 
ments ;  for  which  purpose  he  wiU  find  the  first  part 
of  the  problem,  viz.,  that  of  drawing  curve  and  spiral 
lines  by  hand,  to  be  of  the  utmost  utility  in  forming 
the  general  outline  of  his  design ;  and  for  finishing  the 
smaller  parts,  such  as  raffles,  flowers,  fruit,  &c.,  he 
must  apply  the  knowledge  he  has  acquired  in  drawing 
from  nature,  which  will  complete  his  composition. 


LEAVES. 

Of  the  acanthus,  bear's  breech,  or  brank  ursine, 
there  are  several  species. 

1.  The  moUis,  or  common  bear's  breech,  a  native 
of  Italy. 

2.  The  spinosus,  or  prickly  bear's  breech,  the  leaves 
of  which  are  deeply  jagged  in  very  regular  order,  and 
each  segment  is  terminated  with  a  sharp  spine,  as  is 
also  the  complement  of  the  flower,  which  render  it 
troublesome  to  handle  them. 


112 


ELEMENTS    OF    FOLIAGE. 


3.  The  ilictfolious,  or  shrubby  bear's  breech,  grows 
in  both  the  Indies.  It  is  an  evergreen  shrub,  which 
rises  about  four  feet  high,  and  is  divided  into  many 
branches,  garnished  with  leaves  like  those  of  the  com- 
mon holly,  and  armed  with  spines  in  the  same  man- 
ner ;  the  flowers  are  white,  and  shaped  like  those  of 
the  common  acanthus,  but  smaller. 

4.  The  nigra,  or  Portugal  bear's  breech,  with 
smooth  sinuated  leaves,  of  a  livid  green  color. 

5.  The  middle  bear's  breech,  with  entire  leaves, 
having  spines  on  their  borders. 

EXAMPLE. 
Plate  71 

Shows  the  method  of  beginning  to  draw  leaves,  as 
given  in  the  general  problem  1. 

Suppose  it  were  required  to  draw  or  copy  plate  72, 
either  of  the  same  size,  or  in  any  other  ratio  to  it. 
First  inspect  plate  72,  and  draw  with  a  pencil  a  faint 
curve  line,  circumscribing  the  contour  or  general  out- 
line of  Fig.  1 ;  then  describe  curve  lines  similar  to  it, 
as  at  Fig.  1,  plate  71 ;  then  draw  lines  faintly  with 
a  pencil,  circumscribing  the  compartments  or  divis- 
ions of  Fig.  1,  plate  72 ;  then  draw  lines  in  a  similar 
manner,  as  at  Fig.  1,  plate  71,  observing  that  all  the 
parts  are  similar  to  Fig.  1,  plate  72 ;  next  draw  the 
raffles  and  veins  in  the  compartments  of  Fig.  1,  plate 
71 ;  and,  lastly,  with  a  pen  draw  in  ink  all  the  parts 
of  the  leaf  represented  by  Fig.  1,  plate  72;  then  rub 
your  drawing  clean  ;  the  pencil  lines  wiU  be  rubbed 
out,  and  the  ink  lines  will  be  left,  and  will  represent 
a  figure  similar  to  Fig.  1,  plate  72. 

This  explanation  will  be  sufficient  for  aU  the  fol- 
lowing examples,  however  dissimilar  they  may  be. 
In  the  following  descriptions,  it  wUl  be  only  neces- 
sary to  mention  the  names  of  the  buildings  from 
which  the  examples  were  taken. 


Fig.l 
No.  1. 

Fig.  2 
Athens, 
tlienes. 

No.  2. 


Fig.  1. 
No.  1. 


Plate  72. 

is  taken  from  the  Arch  of  Adrian,  at  Athens. 
The  profile  of  Fig.  1. 

.    From   the  Monument  of  Lysicrates   at 
commonly  called  the  Lantern  of  Demos- 
Profile  of  ditto. 

Plate  73. 

From  the  Temple  of  Pola,  in  Istria. 
Profile  of  ditto. 


Fig.  2.   From  the  Arch  of  Adrian,  at  Athens. 

No.  2.    A  profile  of  ditto. 

Fig.  3.  Elevation  of  a  leaf  taken  from  the  capi- 
tals of  the  columns  on  the  Baths  of  the  Diocletian, 
at  Rome. 

No.  3.   Profile  of  ditto. 


KOSES  IN  THE  CAPITALS  OF  COLUMNS. 

Plate  74. 

Fig.  1.  Elevation  of  the  rose  in  the  abacus  in  the 
Temple  of  Vesta,  at  Tivoli. 

Fig.  2.  The  elevation  of  a  rose  taken  firom  the 
Temple  of  Jupiter  the  Thunderer,  at  Rome. 

Fig.  3.  Elevation  of  a  rose  from  the  abacus  of  the 
capitals  of  the  Temple  of  Vesta,  at  Rome. 

Fig.  4.   Elevation  of  a  rose  in  the  abacus  of  the 

capitals  of  the  pilasters  of  the  frontispiece  of  Nero, 

at  Rome. 

Plate  75. 

Fig.  1.  Elevation  of  a  rose  in  the  abacus  of  the 
capitals  of  the  Arch  of  Titus,  at  Rome. 

Fig.  A.  Elevation  of  a  rose  in  the  abacus  of  the 
capitals  of  the  Pantheon,  at  Rome. 

Figs.  2  and  3  are  designs  for  the  ornaments  of  mo- 
dillions  in  cornices  or  corner  pieces  for  pilasters. 

Plate  76. 

Fig.  1,  the  outline ;  and  Fig.  2,  the  shadowed  leaf 
taken  from  a  frontispiece. 

Plate  77. 

Fig.  1.  From  the  portico  of  the  Temple  of  Anto- 
ninus and  Faustina,  at  Rome. 

Figs.  2, 3,  and  4.   For  corners  and  centres  of  panels. 


ORNAMENTS    FOR    MOULDINGS. 

Plate  7§. 

No.  1.    A  general  outline  of  Example  1. 

No.  2.  The  outline  of  Example  2,  from  the  cima- 
tium  of  the  Temple  of  Minerva  Polias,  at  Priene. 

Example  3.  From  the  cima  recta  in  the  cornice 
of  the  Temple  of  Bacchus,  at  Teos. 


iitSOE^I??  eif  [F®[U1A©1 . 


A':/. 


Fiff.l. 


J7V>      ./ 


Fiff2. 


■^izw. 


l'l.72 


/•'/,/.  J. 


a:-/ 


/■'l: 


.vri'. 


^IW% 


1^" 


'Mme^  (©[?•  i^oiLUtt©^. 


I'l.-. 


Fic/.  I 


:x'?2. 


Fu,.  3. 


I'l.71 


.1"  I 


/■y.f ; 


A".'  '1. 


N^':3. 


\rrn7V  >-7 


E(U€MS!iW©  ®[?  [F®[LQA®i; . 


I'l.; 


a:  I. 


//./.   ■!. 


J?':'. 


^^r^ 


A 


^^^ 


n) 


n.7(i 


iiLiiiiassa'ir©  ®i?  iFOiLOtfiois , 


l'l,77 


I't'/   /. 


'iixh^^^M 


mi 


^44 


/■•„, 


/■}„  -■',. 


n  7is 


SvD5fli;xc)so'uij@tt  m  iF®[LaAisis: . 


Ex<iiii/-/f  / 


^Xirmpjf 


£xi:uiiple     4. 


I'l    7M 


"TOf^nf^ynSc. 


^ 


I  •!,;)(  I 


I 


Mif. . 


/■},/.  / 


fy</.  ■'' 


CARPENTRY. 


113 


Example  4.  From  the  cima  recta  of  the  cornice  of 
the  Temple  of  Peace,  at  Rome. 

Plate  79. 

Fig.  1.  From  the  Arch  of  Titus,  at  Rome. 

Fig.  2.  From  an  impost  moulding  in  the  Arch  of 
Septimius  Severus,  at  Rome. 

Fig.  3.  From  the  cima  recta  of  the  cornice  of  the 
Frontispiece  of  Nero,  at  Rome. 


Plate  80. 

Fig.  1.  The  side,  and  Fig.  2,  the  front,  of  a  key- 
stone of  the  Arch  of  Septimius  Severus,  at  Rome. 

Fig.  3.  The  ichnography  of  the  modillion  in  the 
cornice  of  the  Temple  of  Jupiter  Stator,  at  Rome. 

Fig.  4.  Side  of  the  modillion  in  the  cornice  of  the 
Portico  of  the  Pantheon,  at  Rome. 

Fig.  5.  Ichnography  of  ditto,  inverted. 


CAHPENTRY. 


The  art  of  Carpentry,  in  the  general  acceptation  of  the  term,  in- 
cludes every  method  of  -n-orking  or  employing  timber,  or  its  substi- 
tutes, in  the  construction  of  buildings  ;  but  as  it  is  evident  that 
coarse,  rough  work  requires  very  different  management  from  the 
delicate  finish  of  interior  arrangement,  most  ■writers  have  very  prop- 
erly divided  it  into  two  classes  :  Carpentry,  properly  so  called,  to 
which  belongs  flooring,  roofing,  framing,  and  the  working  of  all 
large  pieces  of  wood ;  and  Joinery,  which  includes  all  ornamental 
works  in  wood,  (except  what  are  obviously  within  the  pro-v'ince  of 
the  cabinet  maker,)  besides  doors,  windows,  sashes,  and  other  objects 
intended  for  close  inspection.  The  former,  of  course,  is  treated  of 
in  this  department. 


THE  ORDER  OF  CARRYING  ON  A  BUILDING  ;  THE  DI- 
JIENSIOXS  OF  THE  TIMBERS  ;  THEIR  DISTANCES, 
AND  PLACES  OF  INSERTION. 

The  designs  of  buildings  being  of  such  a  variety, 
they  not  only  require  various  methods  of  construc- 
tion, but  some  require  appendages  which  are  unne- 
cessary in  others,  and  thus  the  order  of  proceeding 
will  be  varied.  The  order,  however,  of  proceeding 
with  any  description  of  edifice  will  easily  be  under- 
stood, when  that  of  the  usual  manner  is  given. 

Lintellings  very  soon  occur ;  their  thickness  ought 
never  to  be  less  than  as  many  inches  as  the  aperture 
has  feet  in  width.  Some  recommend  that  lintels 
should  be  laid  on  templets ;  but  when  the  mortar 
dries,  this  practice,  though  it  may  seem  to  bind  a 
new  building  together,  is  injurious  to  the  strength  of 
the  walls.  The  old  authors  say  that  bond  timbers 
should  be  dovetailed  at  the  angles ;  but  this  method 
of  joining  timbers  is  not  sufficient  to  prevent,  in  two 
return  walls,  the  one  from  descending,  while  the  other 
keeps  its  place ;  halving  and  bolting  is  much  more 
secure. 

Where  bond  timbers  are  carried  all  round  apart- 
15 


ments  or  rooms,  or  entu-ely  round  a  building,  the 
thickness  of  these  timbers  will  depend  upon  the  mass 
of  the  work  over  tlicm  ;  but  where  they  are  only  par- 
tially inserted  for  finishings,  their  thickness  must  be 
the  thickness  of  a  brick.  Some  old  authors  think  it 
would  not  be  amiss  to  place  bond  timbers  at  the  dis- 
tance of  six  feet  through  the  whole  height  of  the 
building ;  but,  in  our  opinion,  they  ought  to  be  used 
with  great  caution ;  for  as  the  moisture  dries  out  of 
the  timber,  these  ligatures  will  shrink  and  cause  the 
walls  to  bulge,  which  will  not  only  produce  a  very 
unpleasant  effect  to  the  eye,  but  will  endanger  the 
building,  by  weakening  the  walls,  and  make  them 
liable  to  fall.  Therefore,  in  good  work,  bond  timbers 
ought  to  be  dispensed  with  ;  and,  if  necessary,  other 
means  ought  to  be  resorted  to,  which  will  be  equally 
effective  in  point  of  strength ;  but  as  neither  stone 
nor  iron  will  answer  the  purpose  of  fixing,  we  will 
recommend  plugging,  built  in  with  the  brick  work. 


FLOOES. 

We  now  come  to  the  consideration  of  floors.  Li- 
stead  of  mortising  the  ceiling  joists,  we  would  rather 
recommend  to  notch  them  upon,  and  fasten  them  to, 
the  binding  joists  by  means  of  nails.  In  some  single 
joisted  floors,  every  third  or  fourth  joist  is  made 
deeper  than  the  intermediate  joists,  and  the  ceiling 
joists  are  fixed  to  the  deep  joists.  This  construction 
is  adapted  to  the  prevention  of  sound,  by  reason  of 
the  space  which  destroys  or  cuts  off  the  conducting 
power. 


114 


CARPENTRY. 


As  no  timbers  must  enter  a  wall  where  there  arc 
fireplaces  or  flues,  the  ends  of  the  joists,  instead  of 
being  supported  by  the  wall,  must  be  supported  by- 
trimmers  and  trimming  joists.  As  the  trimming 
joists  have  to  support  the  trimmers,  and  these  again 
the  ends  of  the  joists,  the  trimming  joists  should  be 
increased  in  their  thickness  about  one  fifth  part  more 
than  the  breadth  of  a  common  joist. 

In  double  floors,  the  under  sides  of  the  binding 
joists  are  frequently  framed  flush  with  the  under  side 
of  the  girder,  and  about  three  or  four  inches  below 
the  top,  in  order  to  receive  the  bridging  joists.  Some 
old  authors  direct  that  the  bridging  joists  should  be 
pinned  down  to  the  binding  joists  ;  but  this  is  unne- 
cessary, and,  besides,  it  weakens  the  binding  joists  ; 
this  method  is  therefore  inadmissible.  It  w^as  for- 
merly the  practice  to  place  the  binding  joists  about 
three  feet  or  three  feet  six  inches  distant  from  each 
other ;  the  mean  distance  of  the  present  practice  is 
about  five  feet.  Single  floors,  consisting  of  the  same 
quantity  of  timber,  are  much  stronger  than  framed 
floors ;  but  a  preference  is  sometimes  given  to  framed 
floors  in  superior  buildings,  on  account  tliat  they  are 
not  so  liable  to  fracture  the  ceilings,  and  because  they 
conduct  sound  more  imperfectly  than  a  common  joist 
floor ;  and  hence  it  is  that  single  floors  can  only  be 
employed  in  inferior  buildings.  Framed  floors  differ 
from  double  floors  only  in  the  binding  joists  being 
framed  to  girders. 

In  single  floors,  where  the  joists  exceed  eight  feet 
bearing,  pieces  of  board  ought  to  be  inserted  in  the 
spaces  between  the  joists,  in  a  vertical  position,  and 
nearly  the  whole  depth  of  the  joists,  and  in  one  con- 
tinued line  at  right  angles  to  the  joisting.  The  pieces 
of  timber  thus  inserted  are  called  bridges,  and  the 
floor  is  said  to  be  bridged;  the  bridges  ought  not  to  be 
driven  in  with  groat  force,  but  their  ends  should  be  in 
close  contact  with  the  vertical  sides  of  the  joists,  and 
should  be  fixed  thereto  with  a  nail  at  each  end. 

The  bridging  of  a  floor  is  of  great  use,  when  the 
joists  are  thin  and  deep,  in  preventing  their  buckling 
by  pressure;  but  for  this  purpose  there  is  another 
method,  called  keying,  which  consists  of  framing  short 
pieces  of  timber  between  the  joists ;  but  as  the  mor- 
tises which  receive  the  tenons  weaken  the  joists,  and 
as  the  keys  cannot  be  in  a  straight  line,  and  since 
this  method  adda  considerably  to  the  expense,  this 
practice  is  not  so  eligible  as  that  of  bridging.  Single 
joist  flooring  may  be  used  to  any  extent  not  exceed- 


ing sixteen  feet :  but  when  it  is  desirable  to  prcrfcrve 
the  ceiling  free  from  cracks,  and  prevent  the  passage 
of  sound,  a  framed  floor  is  necessary. 

The  ceiling  joists  in  double  floors  arc  generally  put 
in  after  the  building  is  up ;  if,  therefore,  they  are  fixed 
by  means  of  mortises  in  the  sides  of  the  binding 
joists,  to  receive  the  tenons  on  their  ends,  the  space 
between  every  other  two  mortises  must  be  grooved 
out  alternately  upon  the  opposite  sides  of  the  two 
adjacent  binding  joists :  by  this  means,  the  ceiling 
joists  may  easily  be  put  in  their  places,  by  inserting 
the  tenons  in  each  coiling  joist  in  the  mortises  at  one 
end,  and  sliding  the  tenon  on  the  other  end  along  the 
groove  in  the  arc  of  a  circle,  until  the  ceiling  joist 
come  at  a  right  angle  with  the  binding  joist.  The 
long  mortises  or  grooves  in  the  sides  of  the  binding 
joists  are  called  chase  mortises,  or  pulley  mortises. 
The  ceiling  joists  may  be  thirteen  or  fourteen  inches 
apart ;  the  thickness  of  the  bridging  joists  and  ceiling 
joists  need  nqt  be  greater  than  what  is  sufficient  to 
resist  splitting  by  the  driving  in  of  the  nails  in  order 
to  fix  them.  It  has  been  found,  by  experience,  that 
two  inches  is  a  sufficient  thickness  for  the  purpose. 

In  double-framed  floors,  the  distance  of  bridging 
joists,  in  the  clear,  ought  to  be  about  twelve  inches, 
and  should  never  exceed  thirteen.  It  is  a  good  prac- 
tice to  plane  the  upper  edges  of  the  bridging  joists 
straight,  because,  w^hen  the  boarding  is  laid,  the  faces 
for  walking  upon  will  be  more  regular  than  if  the 
boards  had  been  laid  down  upon  the  edges  of  the 
bridging  joists  when  rough  from  the  saw.  The 
straightening  of  the  edges  of  the  bridging  joists  will 
not  only  give  greater  facility  to  the  making  of  a  level 
floor,  but  will  contribute  greatly  towards  making 
sound  work,  and  will  prevent  that  disagreeable 
creaking  noise  which  arises  from  the  parts  not  being 
brought  into  contact ;  for  when  the  tops  of  the  joists 
on  which  the  flooring  boards  are  laid  are  uneven,  it 
wUl  be  impossible  to  avoid  furring  up  the  joists,  or, 
what  is  still  worse,  inserting  chips  in  the  hollows, 
which  will  give  way  in  the  nailing  of  the  boards  to 
the  joists.  The  general  practice  is  to  make  binding 
joists  half  as  thick  again  as  common  joists ;  so  that, 
if  a  common  joist  be  two  inches  thick,  the  binding 
joists  may  be  three  inches  thick. 

Girders  should  always  be  placed  upon  walls  which 
are  solid  underneath  ;  but  when  it  becomes  necessary 
to  lay  them  over  apertures,  the  lintels  should  be  suffi- 
ciently strong  to  support  them.     We  cannot  recom- 


I 
I 


CARPENTRY. 


115 


mend  the  practice  of  laying  girders  obliquely  across 
the  room,  since  it  divides  the  binding  joists  so  very 
uneqvially. 

All  joists  should  be  laid  with  a  camber  upwards, 
so  as  to  raise  the  middle  of  the  floor  about  three 
quarters  of  an  inch  higher  than  the  sides  of  the  room ; 
and  a  similar  observation  applies  to  ceiling  joists, 
viz.,  that  the  under  horizontal  sides  should  rise  with 
a  concavity,  so  that  the  middle  of  the  ceiling  should 
be  three  quarters  of  an  inch  above  the  margins  at  the 
cornices  or  walls.  The  distance  of  girders  from  each, 
or  the  walls,  shovild  never  exceed  twelve  feet. 

Girders  should  always  be  made  of  timber  of 
the  best  quality  that  can  be  found,  and  particularly 


those  which  have  long  bearings. 


When  the  bearing 


exceeds  twenty  feet,  it  is  difficult  to  procure  timber 
of  sufficient  dimensions;  and  the  only  method  is 
to  allow  a  sufficient  thickness  between  the  surface 
of  the  boarding  and  the  ceiling,  since  it  is  found,  by 
experiments  that  have  been  made,  that  a  truss  girder 
is  not  even  so  strong  as  a  solid  beam  of  the  same 
depth.  The  reason  is  obvious,  for  braces  which  have 
only  a  small  inclination  to  the  horizon  throw  the 
most  enormous  compression  on  thek  abutments, 
which  is  liable  to  give  way,  and  the  effect  of  truss- 
ing would  be  rendered  useless ;  but  if  a  sufficient 
height  were  allowed  for  trussing,  girders  might  be 
made  capable  of  supporting  any  weight  whatever. 
Two  feet,  or  even  three  feet,  in  the  height  of  a  build- 
ing, would  be  an  ample  allowance  for  framing  girders 
of  sufficient  strength,  and  would  not  occasion  any 
considerable  expense  to  the  structure,  but  would  give 
solidity  to  the  walls,  by  having  a  greater  distance 
between  the  apertures.  But  where  the  depth  is  lim- 
ited, and  the  bearing  considerable,  girders  ought  to 
be  made  solid,  and  of  cast  iron.  In  order  to  equal- 
ize the  strength  of  solid  girders,  builders  frequently 
cut  them  longitudinally  along  the  middle,  and  turn 
the  ends  of  the  flitches  contrary  to  what  they  were 
at  first  in  the  solid,  and  apply  the  sawn  sides  so 
as  to  face  each  other,  and  then  bolt  the  two  pieces 
together  in  a  sufficient  number  of  intervals;  but 
it  is  evident  that,  since  the  holes  made  for  the 
passing  of  the  bolts  will  weaken  the  timber,  very 
little  strength  will  be  gained.  This  process,  however, 
affords  the  opportunity  of  examining  the  timber,  as, 
in  large  trees,  the  heart  is  frequently  found  in  a  state 
of  decay.  When  this  process  of  reversing  and  bolt- 
ing is  used,  the  tsvo'sawn  sides  of  the  timber  should 
not  be  brought  in  contact,  but  should  be  separated 


by  parallel  pieces  of  wood,  so  as  to  allow  a  sufficient 
circulation  of  air  to  pass  between  the  two  sides  of 
the  flitches  of  the  beams  thus  bolted. 

To  prevent  the  sagging  of  short  girders,  it  is  usual 
to  cut  them  camber ;  that  is,  to  cut  them  with  an 
angle  in  the  middle  of  their  lengths,  so  that  their  cen- 
tres shall  rise  above  the  level  of  their  ends  as  many 
half  inches  as  the  girder  contains  ten  feet  lengths. 
And,  indeed,  girders  of  the  greatest  length,  al- 
though trussed,  should  be  cut  crowning  in  the 
same   manner. 

It  may  be  proper  here  to  notice,  that  the  cambering 
of  girders  does  not  prevent  them  from  sagging,  though 
perhaps  it  may  obviate  their  becoming  concave  on 
the  upper  side.  With  regard  to  trussing  girders,  the 
flitches  should  not  be  cut  to  a  camber,  but  brought 
into  this  state  in  the  ac*^  of  trussing. 


PARTITIONS. 

Partitions  are  usually  lathed  and  plastered;  and 
sometimes  the  spaces  between  the  timbers  are  filled 
with  brick  work.  A  partition  ought  to  be  so  con- 
structed as  to  be  capable  of  supporting  its  own 
weight,  in  whatever  situation  the  door  is  placed,  or 
whether  there  is  a  door  in  the  middle,  or  two  doors 
near  the  ends.  Partitions  that  rest  upon  a  solid  wall 
do  not  require  trussing ;  but  when  there  is  no  sup- 
port, except  at  the  ends,  or  at  two  given  fixed  points, 
the  braces  ought  to  be  so  disposed  as  to  discharge 
the  weight  of  the  whole  mass  upon  these  points ; 
and  it  is  better  to  support  a  partition  by  the  extreme 
walls  it  is  connected  with  than  upon  any  solid  from 
the  bottom ;  for,  in  the  settlement  of  the  walls,  the 
partitions  will  be  carried  along  with  them ;  but  if 
supported  from  the  ground  by  light  materials,  the 
walls  and  partitions  will  descend  unequally,  and 
cause  large  fissures  and  cracks  in  the  ceilings  and  in 
the  plaster  upon  the  walls  and  partitions. 

When  a  partition  is  supported  at  each  end  by 
walls  of  unequal  heights,  the  wall,  which  is  the  most 
ponderous,  will  sink  in  a  much  greater  degree  than 
that  which  is  the  lighter;  therefore,  in  this  case, 
whatever  care  may  be  taken  with  the  framing  of  the 
partitions,  it  will  not  be  possible  to  avoid  the  crack- 
ing and  splitting  of  the  plaster  upon  the  walls  and 
ceiling.  Such  consequences  should  be  guarded 
against  in  the  design  of  the  architect. 


116 


CARPENTRY. 


FRAMING. 

This  mechanical  science  is  divided  into  t^^'•o  princi- 
ples—  the  Scribe  and  the  Square  Rule. 

THE  SCRIBE  RULE. 

1.  First,  the  mortises  should  be  made,  and  the 
faces  got  out  of  wind.  Second,  after  finding  the 
length  of  the  timber  in  which  the  tenons  are  to  be 
made,  for  convenience  apply  the  two-foot  square. 
Third,  take  out  the  size  of  the  mortised  timber  on  the 
end  of  the  square ;  suppose  ten  inches  to  be  the  one 
mortised,  then  fourteen  inches  remain  on  the  square ; 
make  a  distinct  mark  at  the  end  of  the  square,  wliich 
is  called  the  two-feet  mark.  Fourth,  measure  from 
this  mark,  for  the  shoulder,  fifteen  inches,  which 
leaves  one  inch  to  be  scribed;  after  the  tenon  is 
made  and  entered,  the  mortise  and  the  shoulders  are 
brought  together  or  to  a  bearing ;  then  cut  the  shoul- 
ders to  the  scribe,  and  when  put  together  they  will 
remain  out  of  wind,  as  when  scribed.  The  process 
is  generally  applied  to  sills,  posts,  and  principal  rafters. 

2.  A  process  called  tumbling,  is  applied  to  timbers, 
both  ends  of  which  are  to  be  tenoned,  as  girders,  &c. ; 
also  to  sides  and  ends  in  section  framing. 

The  girder  should  be  placed  so  that  both  ends  shall 
come  directly  over  the  lower  end  of  the  mortises. 
For  the  tenons  you  are  about  to  strike,  place  the 
lower  edges  of  the  girder  to  the  line  of  the  lower 
end  of  the  mortises ;  make  a  scratch  on  the  girder  at 
both  ends,  exactly  to  the  face  of  the  mortise.  Cant 
the  girder  so  as  to  leave  those  marks  up ;  fetch  the 
girder  again  over  the  mortise,  and  apply  the  edge  of 
the  square  to  the  face  of  the  mortise,  the  square  ex- 
tending above  the  girder.  Move  the  girder  by  a 
hammer  for  that  purpose,  until  the  scratch  on  the 
corner  of  the  girder  is  brought  to  the  outer  edge  of 
the  square.  Then  with  your  compasses  draw  a  line 
across  the  girder  by  the  edge  of  the  square ;  then 
move  the  square  on  the  opposite  side  of  the  girder, 
and  draw  another  line;  in  the  same  manner  draw 
lines  at  the  other  end  of  the  girder.  Strike  a  line 
across  the  top  and  bottom  of  the  girder,  meeting  the 
end  of  those  which  give  the  exact  length  of  the 
shoulders;  then  strike  the  tenons. 

3.  Cant  or  plumb  marks  are  those  which  are  ap- 
plied to  all  principal  timbers  that  are  to  be  employed 
in  section  framing,  after  having  been  put  together 
in  the  sides.  At  some  part  of  the  post  try  on  the 
square,  and  fit  that  part  (which  may  be  up,  in  the 


laying  out  of  the  section)  to  a  right  angle  with  the 
level  plane  of  the  side  framing,  provided  the  section 
should  be  at  right  angles  with  the  sides.  But  if  the 
section  should  be  required  at  any  other  angle  with 
the  side,  the  plumb  should  be  made  according  to  that 
angle.  The  angle  should  be  taken  with  a  bevel  set 
for  that  purpose  ;  and  on  these  fittings  of  the  posts 
a  right  angle  should  be  struck,  to  guide  the  direction 
of  the  square  across  the  section  framing.  The  posts 
should  be  brought  by  means  of  wedges  in  a  horizon- 
tal plane  across  the  section. 

THE  SQUAHE  RULE. 

This  principle  is  considered  more  simple  than  the 
Scribe  Rule,  as  it  can  be  applied  in  many  cases  with 
less  help  and  more  convenience. 

Li  order  to  make  a  good  frame  of  any  considerable 
magnitude,  it  should  be  the  first  care  of  the  master 
workman  (after  examining  the  plan  of  the  firame  with 
care)  to  make  out  a  proper  schedule  of  the  various 
sizes  of  the  timber.  Set  down  their  appropriate 
marks  on  the  schedule ;  and  when  you  have  finished 
Nos.  1,  2,  &c.,  check  them  on  the  schedule.  It  is  of 
importance  that  all  mortises,  tenons,  pin  holes,  &c., 
should  be  struck  with  a  pattern.  All  the  timber 
should  be  lined  to  its  proper  size,  and  the  mortises 
faced  to  the  same.  Care  should  be  taken  in  applying 
the  pattern ;  for  striking,  it  should  be  governed  by  the 
appropriate  lines.  This  method  has  the  preference 
in  detached  framing ;  the  timber  admitting  of  being 
framed  in  different  places,  and  not  tried  together  until 
its  raising. 


TRUSSES. 

Plate  81. 

Fig.  1  represents  a  truss  partition,  a,  the  truss 
plate,  b,  the  sUl.  c  c,  the  posts,  d,  the  truss  beam. 
e  e,  the  struts.  /  /,  the  studding,  g  g,  the  bridg- 
ing,   h  h  h,  the  door  frames. 

Fig.  2.  Design  for  a  truss  gallery  or  floor. 

Fig.  3.  Method  of  scarfing  and  splicing  timber. 

Fig.  4.  The  horizontal  section  of  Fig.  5. 

Figs.  5  and  6  show  the  best  method  of  trussing 
girders. 

The  king  bolts  through  Figs.  5  and  6  show  the 
two  sides  which  incline  to  each  other  so  as  to  form  a 
wedge,  and  thereby  force  the  trusses  upon  their  abut- 
ments. 


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CARPENTRY. 


117 


To  lighten  the   Girders. 

Having  grooved  the  sides  of  the  flitches  for  the 
trussing  pieces,  so  as  only  to  be  close  at  the  ends, 
about  an  inch  and  a  half  deep  on  each  side,  and 
having  greased  the  head  of  the  lung  bolt,  and  put 
the  whole  slackly  together  sideways  by  the  screws, 
proceed  then  to  turn  the  nut  of  the  Idng  bolt,  and  let 
another  person  strike  the  head  with  a  mallet ;  the 
stroke  will  make  the  king  bolt  start  every  time  it  is 
hit,  and  give  fresh  ease  for  the  turning  of  the  nut.  By 
this  means,  the  girder  may  be  cambered  or  crowned 
at  pleasure  :  the  deflection  from  the  straight  line  is 
generally  one  inch  in  twenty  feet. 

Fig.  7  shows  the  manner  of  joining  the  beam  to 
the  wall  plate. 

Fig.  8.  The  manner  of  keying  the  tenon  through 
the  girder. 

Fig.  9.  Profile  of  the  tusk  tenon. 


PLANS    OF    FLOORS. 

Plate  83. 

Fig.  1.  Plan  of  the  floor,  suitable  for  buildings  of 
any  magnitude. 

a  a  a  a  a,  girders  resting  upon  the  walls,  b  b  b  bi 
binding  joists,  c  c  c,  trimmers,  d  d  d  d  d,  bridging 
joists. 

Fig.  2.  Section  of  the  floor. 

Fig.  3  shows  the  method  of  framing  floors  with 
plank  or  deep  joists. 

a,  the  girder  resting  upon  the  walls,  and  should  be 
10  by  12  inches,  b  b  b  b,  trimmer  joist,  4  by  12 
inches,  e  e  e,  joist,  d  d  d  d,  wall  girders,  6  by  12 
inches,    c  c  c,  bridging  joist,  2  by  12  inches. 

This  floor  is  adapted  to  rooms  16  or  18  feet  square, 
and  the  size  of  the  joist  should  be  12  inches  by  2^  or 
3  inches. 


.    DESIGNS    FOR    ROOFS. 

A  roof,  in  architecture,  is  a  cover  of  a  building  for 
protecting  its  inhabitants  from  disagreeable  changes 
of  weather,  and  from  the  depredations  of  evil-dis- 
posed persons ;  but  a  roof  in  carpentry  is  the  timber 
framing  made  to   support  the   actual  covering  of 


boards,  shingles,  slate,  lead,  &c.  As  the  roof  may 
be  made  one  of  the  principal  ties  of  a  building,  it 
should  not  be  made  too  heavy  to  burden  the  walls, 
nor  too  light  to  be  incapable  of  keeping  them  to- 
gether. 

The  principal  timbers  of  a  roof  arc  the  wall  plates, 
tie  beams,  principal  rafters,  common  rafters,  pole 
plates,  purlines,  king  posts,  queen  posts,  struts,  strain- 
ing beams,  strong  sUls,  &c.  Hence,  since  the  pres- 
sure of  the  roof  is  wholly  discharged  upon  the  wall 
plates,  these  should  be  made  of  sufficient  thickness 
and  breadth  to  distribute  the  weight  of  the  roof  to 
the  best  advantage. 

Plate  83. 

Fig.  1,  a  a  a  a,  wall  plate ;  b  b,  jack  beams;  c  c  c  c, 
tie  beams ;  d  d,  ridge  line  and  jack  beam ;  e  e  e  e, 
dragon  piece  ;  ////,  angle  tie ;  g-  g-  g,  hip  rafters  ; 
h  h,  jack  rafters ;  i  i,  principal  rafters  ;  j,  king  post ; 
k  k,  strut  braces. 

To  find  the  length  and  backing  of  hip  rafters. 

Draw  7,  4,  8,  the  base  lines ;  then  draw  4,  5,  at 
right  angles  with  8,  4,  which  will  give  the  perpen- 
dicular height  of  the  backing  of  the  hip  rafter. 
From  9,  extend  one  foot  of  the  dividers  to  10 ;  de- 
scribe the  arc,  cutting  the  base  line  at  2 ;  then  the 
lines  from  2  to  1  and  from  2  to  3  give  the  angle 
required  for  the  backing,  c,  a  section  of  the  hip 
rafter. 

To  find  the  angle  and  intermediate  ribs  of 
octagon  roofs. 
Fig.  2  is  the  plan  of  an  octagon  dome,  a  b  being 
the  base  line  of  the  given  rib.  No.  2  shows  the 
curve  of  the  dome,  in  this  case  half  of  a  circle 
drawn  from  the  centre  a.  Draw  a  1,  cutting  the 
circle  at  1  and  at  right  angles  with  d  b,  and  produce 
it  to  a ;  divide  b  1  into  seven  or  more  equal  parts. 
Make  a  b  No.  3  parallel  and  equal  to  a  b  No.  1,  b  e 
equal  to  6  c  No.  1,  and  draw  e  a.  Then  draw  ordi- 
nates  from  a  b  No.  2  to  a  e  No.  3,  parallel  to  a  1, 
cutting  the  circle  in  No.  2  at  2,  3,  4,  5,  6,  7,  and  a  e 
No.  3  at  2,  3,  4,  5,  6,  7.  Draw  a  1  at  right  angles 
with  a  e,  also  2  2,  3  3,  4  4,  5  5,  6  6,  and  7  7,  parallel 
to  a  1,  and  equal  to  7  7,  6  6,  5  5,  4  4,  3  3,  2  2,  and 
a  1  in  No.  2,  and  then  trace  the  curve  c  7  6  5  4  3  2 
and  1,  which  will,  when  placed  in  its  right  position, 
correspond  with  the  given  circle. 


118 


CARPENTRY. 


To  find  the  form  of  a  board  to  bend  upright  to 
the  crown. 

Fig.  2.  Produce  the  line  a  fto  e  No.  1.  Take  the 
divisions  2  3  4  5  6  7  on  the  curve  line  b  1  No.  2,  and 
lay  them  from  /  in  F  along  the  line  1111,  &c.,  to 
e;  then  the  line/e  No.  1  will  be  equal  to  the  curve 
line  i  1  No.  2.  Transfer  the  ordinates  2  3  4  5  6  7  in 
the  angle  a  b  e  No.  3,  and  lay  them  from  /  in  F 
No.  1  along  the  Ime  1111,  &c.,  at  right  angles  with 
the  line/e,  and  set  them  off  on  each  side  to  1  7, 1  7, 
1  6,  1  6,  1  5,  1  5,  1  4, 1  4, 1  3, 1  3,  and  1  2, 1  2. 

Those,  when  traced,  will  give  the  form  of  the 
board  F. 

Fig.  3.  An  octagon  roof  of  a  different  curvature 
from  that  represented  in  Fig.  2,  but  is  formed  on  the 
same  principles. 

Plates   84,  85. 

On  plate  Nos.  84  and  85  we  have  given  designs  for 
framing  large  roofs  without  wooden  king  or  queen 
posts,  substituting  iron  rods  in  their  stead.  To 
whom  we  are  indebted  for  this  method  of  framing 
we  have  not  been  able  to  learn  with  any  degree  of 
certainty.  It  may,  however,  be  considered  of  quite 
modern  invention  ;  for,  as  the  result  of  a  careful  in- 
vestigation, we  have  found  no  example  of  longer 
standing  than  thirty  years,  and  have  not  found  the 
idea  in  any  published  work,  with  the  exception  of 
some  of  the  recent  writings  of  the  late  Asher  Ben- 
jamin, Esq.  This  method  was  vised  by  him  as  early 
as  the  year  1828,  and  after  that  time  it  was  intro- 
duced into  nearly  all  the  large  roofs  he  constructed  ; 
and  although  he  may  not  have  been  the  first  who 
has  used  it,  yet,  as  far  as  we  can  learn,  he  has  done 
as  much  as  any  other  person  to  introduce  it  into 
general  use.  It  was  published  by  him  in  his  Build- 
er's Guide,  in  1839,  and  the  principle  involved  has 
received  the  approbation  of  nearly  all  the  principal 
architects  of  Boston.  Mr.  Charles  G.  Hall,  archi- 
tect of  this  city,  adopted  it  some  eighteen  years 
since,  and  used  it  in  some  of  the  largest  buildings  in 
this  vicinity.  The  roof  over  the  large  hall  of  the 
Fitchburg  depot,  in  this  city,  is  a  fine  example  of 
this  method  of  framing,  and  has  fully  dcmonstr,ated 
its  utility.  The  floor  of  this  hall  is  166  feet  long, 
and  76  feet  wide,  and  is  entirely  supported  by  the 
roof.  On  the  occasion  of  one  of  Jenny  Lind's  con- 
certs which  was  held  there,  it  was  filled,  together 


with  the  large  passage,  to  its  utmost  capacity,  which, 
according  to  the  experiments  of  Tredgegold,  Rennie, 
etc.,  was  no  less  than  the  enormous  weight  of 
1,873,960  pounds,  or  nearly  937  tons ;  and,  so  far  as 
can  be  ascertained,  this  roof  resisted  the  immense 
strain  without  any  material  settlement.  Although 
by  this  system  no  new  principle  is  established,  yet  it 
may  be  looked  upon  as  one  of  the  most  successful 
achievements  in  the  science  of  carpentry,  and  it  has 
added  as  much  to  the  science  as  did  the  arch  to 
masonry.  It  has  been  introduced  in  many  forms, 
and  employed  in  many  ways  ;  and  in  every  case 
where  a  due  propriety  has  been  observed  in  regard  to 
the  size  of  timber  employed  in  the  truss,  it  has  given 
entire  satisfaction.  But  the  great  simphcity  of  the 
theory  has,  in  some  cases,  led  to  its  abuse  ;  and  as  an 
illustration  of  this,  we  have  but  to  refer  to  a  design 
for  an  arched  roof  as  constructed  by  the  author  of 
the  Builder's  Guide,  and  shown  on  plate  64  of  that 
work.  In  this  example  are  two  rods,  some  forty  feet 
long,  and  they  must  necessarily  be  expanded  so 
much  by  the  heat  of  oux  summer  as  to  relieve  itself 
from  the  strain  it  is  intended  to  support,  so  that  at 
times  the  whole  weight  must  come  directly  on  the 
tie  beams,  which  would  materially  loosen  the  whole 
truss.  We  speak  of  this  with  all  deference  to  the 
knowledge  and  experience  of  the  author,  yet  we  can- 
not see  that  the  experiment  can  philosophically  rec- 
ommend itself  in  a  roof  of  seventy  feet  span.  We 
are  aware  that  the  sanie  objection  can  be  brought  to 
a  certain  degree  against  the  whole  theory  of  substi- 
tuting rods  for  the  posts  ;  yet  when  we  take  into  con- 
sideration the  fact  that,  in  nearly  all  roofs  framed  with 
rods  in  the  ordinary  way,  the  purlines  are  well  sup- 
ported by  the  large  truss  rafter  and  the  collar  beam,  — 
that  the  truss  without  the  rods  would,  if  well  executed, 
almost  sustain  itself,  and  that  the  rods  are  not  only 
proportionably  shorter,  but  differently  applied,  —  we 
cannot  see  that  any  fears  need  be  entertained  in  case 
of  the  latter,  as  may  be  with  the  former.  With  a  de- 
gree of  propriety,  therefore,  and  an  adherence  to  the 
principles  of  strength  and  support,  the  new  method 
may  be  used  in  an  endless  variety  of  ways ;  and 
there  is  now  no  reasonable  excuse  for  the  uneven 
roofs  which  are  so  often  presented  to  view  in  many 
of  our  churches  and  other  large  buildings.  —  Editors. 

Plate    86. 

Fig.  A  shows  how  to  glue  up  the  head  of  a  niche 


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STAIRS. 


119 


in  five  or  more  blocks,  or  rings,  according  as  the 
workmen  shall  deem  expedient. 

Fig.  B  is  the  plan  of  a  circular  dome;  C  the  sec- 
tion, which  shows  at  d  and  d  how  to  square  the  pur- 
lines,  so  as  to  make  them  tend  to  the  centre,  or  to 
stand  square  to  the  surface  of  the  dome ;  but  there 
is  not  the  least  occasion  for  the  squaring  of  any  pur- 
lines,  which  is  attended  with  a  deal  of  trouble  and 
waste  of  stuff;  you  need  only  to  get  them  out  of  the 
same  curve  as  that  of  a  great  circle  of  a  sphere,  of 
which  the  dome  is  a  segment,  and  quite  square  at 
the  same  time,  which  purlmes  being  fixed  between 
the  ribs,  the  middle  of  them  will  be  above  the  level 
at  the  joints,  but  will  be  in  the  true  surface  of  the 
dome,  and  stand  in  a  plane  surface  to  the  centre. 

To  find  the  form  of  a  board  to  bend  upright 
to  the  crown. 

Divide  E  into  eight  parts ;  that  is,  one  quarter  or 
any  other  number  —  the  more  the  truer ;  set  one  on 
the  outside  of  1  1  1,  &:c. ;  draw  7  e  and  1  e  to  e  in 
the  centre ;  take  the  divisions  12  3  4,  &c.,  round  E, 
and  lay  them  from  8,  in  F,  along  the  line  1111,  &c. ; 
then  circle  them  round  e,  and  take  1 1,  1  2,  1  3,  &c. 
in  E,  and  set  them  off  on  each  side  to  1 1,  1 1, 1  2, 
1  2,  1  3,  1  3,  &c. ;  those,  when  traced,  will  give  the 
form  of  the  board  F. 


To  find  the  centres  for  bending  the  boards 
horizontal  in  D. 

It  is  evident,  the  more  parts  any  thing  of  this  na- 
ture is  divided  into,  the  truer  it  will  be ;  but  I  shall 
only  divide  into  four,  for  the  sake  of  eonvcniency. 
Draw  4  3,  to  meet  the  perpendicular  at  d ;  and  3  2, 
to  meet  at  c,  &c. ;  then  d  c  b  a  will  be  the  centres  for 
the  boards  G,  H,  I,  K. 

Fig.  C  is  a  method  of  finding  the  length  and  bevel 
of  hip  and  jack  rafters. 

Tlie  Hip  Rafter.  —  a  bis  the  base  line ;  c  the  per- 
pendicular height ;  draw  a  line  ac;  then  c  is  the  bevel 
at  the  highest  point  of  the  king  post,  a  the  bevel  at 
the  beam,  and  a  c  the  length  of  the  hip  rafter. 

To  find  the  bevel  and  length  of  the  jack  rafters. 

d  e  is  the  base  line,  e  f  the  height  equal  to  eg; 
then  d  e  gis  the  right  angle ;  describe  an  arc  g  h,  of 
which  dg  is  the  radius,  cutting  a  b  at  h ;  then  draw 
the  line  hd;  gis  the  down  bevel,  and h  the  top  bevel, 
and  h  d  is  the  length  of  the  jack  rafter. 

For  this  method  of  finding  the  length  and  bevel  ol 
jack  rafters  I  am  indebted  to  the  politeness  of  Mr. 
Salmon  Washburn,  whose  skill  and  ingenuity  first 
discovered  this  mode,  which  has  met  with  the  decid- 
ed approbation  of  the  few  to  whom  it  has  been  com- 
municated ;  and  it  is  now  published  for  the  first  time. 


STAIRS. 


This  is  one  of  the  most  important  subjects  connected  with  the  art 
of  building,  and  should  he  attentively  considered,  not  only  with 
regard  to  the  situation,  but  as  to  the  design  and  execution.  The 
convenience  of  the  building  depends  on  the  situation,  and  the 
elegance  on  the  design  and  execution  of  the  workmanship.  In  con- 
triving a  grand  edifice,  particular  attention  must  be  paid  to  the  sit- 
uation of  the  space  occupied  by  the  stairs,  so  as  to  give  them  the 
most  easy  command  of  the  rooms. 

"  Staircases,"  says  Palladio,'  "  will  be  commendable  if  they  are 
clear,  ample,  and  commodious  to  ascend,  inviting,  as  it  were,  people 
to  go  up.  They  will  he  clear  if  they  have  a  bright  and  equally  dif- 
fuse light;  they  will  be  sufficiently  ample  if  they  do  not  seem 
scanty  and  narrow  to  the  size  and  quality  of  the  fabric.  But  they 
should  never  be  less  than  four  feet  in  width,  that  two  persons  may 
pass  each  other.  They  will  bo  convenient  with  respect  to  the  whole 
building  if  the  arches  under  them  can  bo  used  for  domestic  pur- 
poses ;  and  witli  respect  to  persons,  if  their  ascent  is  not  too  steep 
and  difficult,  to  avoid  which,  the  steps  should  be  t'wicc  as  broad  as 
high. 


With  regard  to  the  lighting  of  a  good  staircase,  a 
skylight,  or,  rather,  lantern,  is  the  most  appropriate, 
for  these  unite  elegance  with  utility ;  that  is,  admit 
a  powerful  light,  with  elegance  in  the  design.  In- 
deed, where  the  staircase  does  not  adjoin  the  exterior 
wall,  this  is  the  only  light  that  can  be  admitted. 
Where  the  height  of  a  story  is  considerable,  resting- 
places  are  necessary,  which  go  under  the  name  of 
quarter  paces  and  half  ptaces,  according  as  the  pas- 
senger has  to  pass  one  or  two  right  angles  ;  that  is, 
as  he  has  to  describe  a  quadrant  or  semicircle.  In 
very  high  stories,  which  admit  of  sufficient  head 
room,  and  where  the  space  allowed  for  the  staircase 
is  confined,  the  staircase  may  have  two  revolutions 
in  the  height  of  one  story,  which  will  lessen   the 


120 


STAIRS. 


height  of  the  steps ;  but  in  grand  staircases  only 
one  revolutiou  can  be  admitted,  the  length  and 
breadth  of  the  space  on  the  plan  being  always  pro- 
portioned to  the  height  of  the  building,  so  as  to 
admit  of  fixed  proportions. 

The  breadth  of  the  steps  ought  never  to  be  more 
than  fifteen  inches,  nor  less  than  nine  ;  the  height  not 
more  than  eight,  nor  less  than  five.  There  are  cases, 
however,  which  are  exceptions  to  all  rule.  When 
the  height  of  the  story  is  given  in  feet,  and  the 
height  of  the  step  in  inches,  you  may  throw  the  feet 
into  inches,  and  divide  it  by  the  number  of  inches 
the  step  is  high,  and  the  quotient  will  give  the  num- 
ber of  steps. 

It  is  a  general  maxim,  that  the  greater  breadth  of 
a  step  requires  less  height  than  one  of  less  breadth. 
Thus,  a  step  of  12  inches  in  breadth  will  require  a 
rise  of  7  inches,  which  may  be  taken  as  a  standard 
to  reffulate  those  of  other  dimensions. 

Though  it  is  desirable  to  have  some  criterion  as  a 
guide  in  the  arrangement  of  a  design,  yet  workmen 
will,  of  course,  vary  them  as  circumstances  may  re- 
quire. Stairs  are  constructed  variously,  according  to 
the  situation  and  destination  of  the  buildmg. 

Geometrical  stairs  are  those  which  are  supported 
by  having  one  end  fixed  in  the  wall,  and  every  step 
in  the  ascent  having  an  auxiliary  support  from  that 
immediately  below  it,  and  the  lowest  step  from  the 
floor. 

Bracket  stairs  are  those  which  have  an  opening  or 
well  with  strings  and  newels,  and  are  supported  by 
landings  and  carriages.  The  brackets  are  mitred  to 
the  ends  of  each  riser,  and  are  fixed  to  the  string 
board,  which  is  moulded  below  like  an  architrave. 

Dog-legged  stairs  are  those  which  have  no  opening 
or  well  hole,  and  have  the  rail  and  balusters  of  both 
the  progressive  and  returning  flights  falling  in  the 
same  vertical  planes,  the  steps  being  fLxed  to  strings, 
newels,  and  carnages,  and  the  ends  of  the  steps  of 
the  inferior  kind  terminating  only  upon  the  side  of 
the  string,  without  any  nosing.  In  taking  dimen- 
sions and  laying  down  the  plan  and  section  of  stair- 
cases, take  a  rod,  and,  having  ascertained  the  num- 
ber of  steps,  mark  the  height  of  the  story  by  stand- 
ing the  rod  on  the  lower  floor ;  divide  the  rod  into  as 
many  equal  parts  as  there  arc  to  be  risers ;  then,  if 
you  have  a  level  surface  to  work  upon  below  the 
stair,  try  each  of  the  risers  as  you  go  on,  and  this 
will  prevent  any  excess  or  defect ;  for  any  error,  how- 


ever small,  when  multiplied,  becomes  of  considerable 
magnitude,  and  even  the  dilTerence  of  an  inch  in  the 
last  riser  will  not  only  have  a  bad  effect  to  the  eye, 
but  will  be  apt  to  confuse  persons  not  thinking  of 
any  such  irregularity.  In  order  to  try  the  steps 
properly  by  the  story  rod,  if  you  have  not  a  level 
surface  to  work  from,  the  better  way  will  be  to  lay 
two  rods  on  boards,  and  level  their  top  surface  to 
that  of  the  floor.  Place  one  of  these  rods  a  little 
within  the  string,  and  the  other  near  or  close  to  the 
wall,  so  as  to  be  at  right  angles  to  the  starting  line 
of  the  first  riser,  or,  which  is  the  same  thing,  parallel 
to  the  plan  of  the  string ;  set  off"  the  breadth  of  the 
steps  upon  these  rods,  and  number  the  risers;  you 
may  set  not  only  the  breadth  of  the  fliers,  but  that 
of  the  winders  also.  In  order  to  try  the  story  rod 
exactly  to  its  vertical  situation,  mark  the  same 
distances  of  the  risers  upon  the  top  edges  as  the 
distances  of  the  plan  of  the  string  board  and  the 
rods  are  firom  each  other. 

In  bracket  stairs,  as  the  internal  angle  of  the  steps 
is  open  to  the  end,  and  not  closed  by  the  string  as  in 
common  dog-legged  stairs,  and  the  neatness  of  work- 
manship is  as  much  regarded  as  in  geometrical  stairs, 
the  balusters  must  be  neatly  dovetailed  into  the  ends 
of  the  steps,  two  in  every  step.  The  face  of  each 
front  baluster  must  be  in  a  straight  surface  with  the 
face  of  the  riser,  and,  as  all  the  balusters  must  be 
equally  divided,  the  face  of  the  middle  baluster  must 
stand  in  the  middle  of  the  face  of  the  riser  of  the 
preceding  step  and  succeeding  one.  The  risers  and 
heads  are  all  previously  blocked  and  glued  together, 
and,  when  put  up,  the  under  side  of  the  step  nailed 
•or  screwed  into  the  under  edge  of  the  riser,  and  then 
rough  brackets  to  the  rough  strings,  as  in  dog-legged 
stairs,  the  pitching  pieces  and  rough  strings  being 
similar.  In  gluing  up  the  steps,  the  best  method  is 
to  make  a  templet,  so  as  to  fit  the  external  angle  of 
the  steps  with  the  nosing. 

The  steps  of  geometrical  stairs  ought  to  be  con- 
structed so  as  to  have  a  very  light  and  clean  appear- 
ance when  put  up ;  for  this  purpose,  and  to  aid  the 
principle  of  strength,  the  risers  and  treads,  when 
planed  up,  ought  not  to  be  less  than  one  eighth  of 
an  inch,  supposing  the  going  of  the  stair  or  length 
of  the  step  to  be  four  feet ;  and  for  every  six  inches 
in  length,  another  one  eighth  may  be  added.  The 
risers  ought  to  be  dovetailed  into  the  cover,  and, 
when  the  steps  are  put  up,  the  treads  are  screwed  up 


STAIRS. 


121 


from  oclow  to  the  under  edge  of  the  risers.  The 
holes  for  sinlciiig  the  heads  of  the  screws  ought  to 
be  bored  with  a  centre  bit,  then  fitted  closely  in  with 
wood,  well  matched,  so  as  entu-cly  to  conceal  the 
screws,  and  appear  as  one  uniform  surface.  Brack- 
ets are  mitred  to  the  riser,  and  the  nosings  are  con- 
tinued round.  In  this  mode,  however,  there  is  an 
apparent  defect ;  for  the  brackets,  instead  of  giving 
support,  are  tliemselvcs  unsupported  and  dependent 
on  the  steps,  being  of  no  other  use,  in  point  of 
strength,  than  merely  tying  the  sisers  and  treads  of 
the  internal  angles  of  the  step  together;  and,  from 
the  internal  angles  being  hollow,  or  a  reentrant 
angle,  except  at  the  ends,  which  terminate  by  the 
wall  at  one  extremity,  and  by  the  brackets  at  the 
other,  there  is  a  want  of  regiilar  finish.  The  cavetto 
or  hollow  is  carried  round  the  fi-ont  of  the  riser,  and 
is  returned  at  the  end  and  mitred  round  the  bracket ; 
and  if  an  open  string,  —  that  is,  the  under  side  of  the 
stairs  open  to  view, — the  hollow  is  continued  along 
the  angle  of  the  step  and  riser. 

The  best  plan,  however,  of  constructing  geometri- 
cal stairs,  is  to  put  up  the  strings,  and  to  mitre  the 
brackets  to  the  risers,  as  usual,  and  enclose  the  soffit 
with  lath  and  plaster,  which  will  form  an  inclined 
plane  under  each  flight,  and  a  winding  surface  under 
the  winders.  Lr  superior  staircases,  for  the  best 
buildings,  the  soffit  may  be  divided  into  panels.  K 
the  risers  are  made  from  two-inch  planks,  it  will 
greatly  add  to  the  solidity. 

Li  constructing  a  flight  of  geometrical  stairs  where 
the  soffit  is  enclosed  as  above,  the  bearers  should  all 
be  fi-amed  together,  so  that,  when  put  up,  they  will 
form  a  perfect  staircase.  Each  piece  of  framework 
which  forms  a  riser  should,  in  the  partition,  be  well 
wedged  at  the  ends.  This  plan  is  always  advisable 
when  strength  and  firmness  are  requisite,  as  the  steps 
and  risers  are  entirely  dependent  on  the  framed  car- 
riages, which,  if  carefully  put  together,  will  never 
yield  to  the  greatest  weight. 

In  preparing  the  string  for  the  \\Teath  part,  a 
cylinder  should  be  made  of  the  size  of  the  well-room 
of  the  stau-case,  which  can  be  done  at  a  trifling  ex- 
pense ;  then  set  the  last  tread  and  riser  of  the  fliers 
on  one  side,  and  the  first  tread  and  riser  of  the  re- 
turning flight  on  the  opposite  side,  at  their  respective 
heights ;  then,  on  the  centre  of  the  curved  surface  of 
this  cylinder,  mark  the  middle  between  the  two,  and 
with  a  thin  slip  of  wood  bent  round  with  the  ruling 


edge,  cutting  the  two  nosings  of  these  fliers,  and, 
passing  through  the  intermediate  height  marked  on 
the  cylinder,  draw  a  line,  which  will  give  the  wreath 
line  formed  by  the  nosmgs  of  the  winders;  then 
draw  the  whole  of  the  winders  on  this  line  by 
dividing  it  into  as  many  parts  as  you  want  risers, 
and  each  point  of  division  is  the  nosing  of  such 
winder.  Having  thus  far  proceeded,  and  carefully 
examined  your  heights  and  widths,  so  that  no  error 
may  have  occurred,  prepare  a  veneer  of  the  width 
intended  for  your  string,  and  the  length  given  by  the 
cylinder,  and,  after  laying  it  in  its  place  on  the  cylin- 
der, proceed  to  glue  a  number  of  blocks  about  an 
inch  wide  on  the  back  of  the  veneer,  with  their 
fibres  parallel  to  the  axis  of  the  cylinder.  When 
dry,  this  wiU  form  the  string  for  the  wreath  part  of 
the  staircase,  to  be  framed  into  the  straight  strings. 
It  is  here  necessary  to  observe,  that  about  five  or  six 
inches  of  the  straight  string  should  be  in  the  same 
piece  as  the  circular,  so  that  the  joints  fall  about  the 
middle  of  the  first  and  last  fliers.  This  precaution 
always  avoids  a  cripple,  to  which  tlie  worlc  w'ould 
otherwise  be  subject. 

The  branch  of  stair  building  that  falls  under  our 
next  and  last  consideration  is  that  of  hand  railing, 
which  calls  into  action  all  the  ingenuity  and  skill  of 
the  workman.  This  art  consists  in  constructing 
hand  rails  by  moulds,  according  to  the  geometrical 
principles,  that,  if  a  cylinder  be  cut  in  any  direction 
except  parallel  to  the  axis  or  base,  the  section  will 
be  an  ellipsis  ;  if  cut  parallel  to  the  axis,  a  rectangle ; 
and  if  parallel  to  the  base,  a  circle. 

Now,  suppose  a  hollow  cylinder  be  made  to  the 
size  of  the  weU-room  of  the  staircase,  the  interior 
concave  and  the  exterior  convex,  and  the  cylinder  be 
cut  by  any  inclined  or  oblique  plane,  the  section 
formed  will  be  bounded  by  two  concentric  similar 
ellipses ;  consequently,  the  section  wUl  be  at  its 
greatest  breadth  at  each  extremity  of  the  larger  axis, 
and  its  least  breadth  at  each  extremity  of  the  smaller 
axis.  Therefore,  in  any  quarter  of  the  ellipsis  there 
will  be  a  continued  increase  of  breadth  from  the 
extremity  of  the  lesser  axis  to  that  of  the  greater. 
Now,  it  is  evident  that  a  cylinder  can  be  cut  by  a 
plane  tlu-ough  any  three  points ;  therefore,  supposing 
we  have  the  height  of  the  rail  at  any  three  points  in 
the  cylinder,  and  that  we  cut  the  cylinder  through 
these  points,  the  section  wiU  be  a  figure  equal  and 
similar   to  the   face  mould  of  the  rail ;  and  if  the 


122 


STAIRS. 


cylinder  be  cut  oy  another  plane  parallel  to  the  sec- 
tion, at  such  a  distance  from  it  as  to  contain  the 
thickness  of  the  rail,  this  portion  of  the  cylinder  wiU 
represent  a  part  of  the  rail  with  its  vertical  siu'faccs 
already  worked :  and  again,  if  the  back  and  lower  sur- 
face of  this  cyliiidi'ic  portion  be  squared  to  vertical 
lines,  either  on  the  convex  or  concave  side,  through 
two  certain  parallel  lines  drawn  by  a  thin  piece  of 
wood,  which  is  bent  on  that  side,  the  portion  of  the 
cylinder  thus  formed  will  represent  the  part  of  the 
rail  intended  to  be  made. 

Though  the  foregoing  only  relates  to  cylindrical 
well-rooms,  it  is  equally  applicable  to  raUs  erected  on 
any  seat  whatever. 

The  face  mould  applies  to  the  two  faces  of  the 
plank,  and  is  regulated  by  a  line  drawn  on  its  edge, 
which  line  is  vertical  when  the  plank  is  elevated  to 
its  intended  position.  This  is  also  called  the  raking 
mould. 

The  falling  mould  is  a  parallel  piece  of  thin  wood 
applied  and  bent  to  the  side  of  the  raU  piece,  for  the 
purpose  of  drawing  the  back  and  lower  surface,  which 
should  be  so  formed  that  every  level  straight  line  di- 
rected to  the  axis  of  the  well-room,  from  every  point 
of  the  side  of  the  rail  formed  by  the  edges  of  the  fall- 
ijig  mould,  coincide  with  the  surface. 

Li  order  to  cut  the  portion  of  raU  required  out  of 
the  least  possible  thickness  of  stuff,  the  plank  is  so 
turned  up  on  one  of  its  angles  that  the  upper  surface 
is  nowhere  at  right  angles  to  a  vertical  plane  passing 
through  the  chord  of  the  plane ;  the  plank  in  this  po- 
sition is  said  to  be  sprung. 

The  pilch  board  is  a  right-angled  ti-iangular  board 
made  to  the  rise  and  tread  of  the  step,  one  side  form- 
ing the  right  angle  of  the  width  of  the  tread,  and  the 
other  of  the  height  of  the  riser.  When  there  are  both 
winders  and  fliers,  two  pitch  boards  must  be  made 
to  their  respective  treads,  but,  of  course,  of  the  same 
height,  as  all  the  steps  rise  the  same. 

The  bevel  by  which  the  edge  of  the  plank  is  re- 
duced from  the  right  angle  when  the  plank  is  sprung, 
is  termed  the  spring  of  the  plank,  and  the  edge  thus 
bevelled  is  called  the  sprung  edge. 

The  bevel  by  which  the  face  mould  is  regulated  to 
each  side  of  the  plank  is  called  the  pitch. 

The  formation  of  the  upper  and  lower  surface  of 
a  rail  is  called  tlie  falling  of  the  rail;  the  upper  sur- 
face of  the  rail  is  termed  the  hack. 

In  the  construction  of  hand  rails,  it  is  necessary  to 


spring  the  plank,  and  then  to  cut  away  the  super- 
fluous wood,  as  directed  by  the  drawings,  formed  by 
the  face  mould,  which  may  be  done  by  an  expe- 
rienced workman  so  exactly  with  a  saw  as  to  require 
no  further  reduction ;  and  when  set  in  its  place,  the 
surface  on  both  sides  will  be  vertical  in  all  parts,  and 
in  a  surface  perpendicular  to  the  plan.  In  order  to 
form  the  back  and  lower  surface,  the  falling  mould  is 
applied  to  one  side,  generally  the  convex,  in  such  a 
manner  that  the  upper  edge  of  the  falling  mould  at 
one  end  coincides  with  the  face  of  the  plank,  and 
the  same  in  the  middle,  and  leaves  so  much  wood  to 
be  taken  away  at  the  other  end  as  will  not  reduce 
the  plank  on  the  concave  side ;  the  piece  of  wood  to 
be  thus  formed  into  the  wreath  or  twist  being  agree- 
able to  their  given  heights. 

Plate   87. 

To  find  the  projection  of  a  helinet,  on  a  plane 
parallel  to  the  axis  of  the  cylindromc  and  per- 
pendicular to  the  cutting  plane  of  the  solid. 

Figs.  3  and  4.  Let  A  B  C  D  E  F  G  H  I  K  L  M  A, 
(Fig.  3,)  be  the  plan  of  a  helinet,  the  quadrantal  part 
being  B  CDEFGHIKLB,  and  the  straight 
part  being  A  B  L  M  A. 

Let  Fig.  4  be  the  falling  mould,  corresponding  to 
the  concave  side  of  the  semi-cycloid,  found  in  the 
usual  manner,  viz.,  draw  any  straight  line  X  V  W  u; 
make  U  V  equal  to  the  breadth  of  one  of  the  fliers, 
and  V  X  equal  to  the  stretch  of  B  F ;  draw  X  n  per- 
pendicular to  U  X,  equal  to  the  height  of  as  many 
winders  as  are  contained  in  the  circular  part,  together 
wdth  the  height  of  the  flier ;  draw  V  t  perpendicular 
to  U  X,  equal  in  height  to  a  step,  and  join  t  n;  then 
complete  the  falling  mould,  of  which  the  under  edge 
i&n  0  p  qr  aV,  and  the  upper  edge  z  s  <  M  V  W  X ; 
make  V  W  equal  to  B  A,  in  Fig.  3  ;  di-aw  W  a  per- 
pendicular to  X  U,  cutting  the  under  side  of  the  fall- 
ing moidd  at  «,  and  «/ parallel  to  U  X;  then  a  /  is 
the  stretch  of  A  B  C  D  E  F,  Fig.  3.  In  Fig.  3,  di- 
vide the  quadrant  B  F  into  any  equal  parts,  B  C, 
C  D,  D  E,  E  F,  which  stretch  upon  a  f  Fig.  4,  ac- 
cording to  the  corresponding  letters.  In  Fig.  3,  bisect 
C  D  at  I ;  ch-aw  I  P  radiating  to  the  centre  N,  cut 
ting  the  convex  side  of  the  plan  at  P ;  draw  F  P  R 
and  F  O  and  P  Q.  parallel  to  each  other,  making  an 
angle  with  F  R.  In  Fig.  4,  bisect  c  d  in  y,  and  draw 
y  y  perpendicular  to  a  f  uniting  the  under  edge  of 
the  falling  mould  at  y ;  divide  fn  and  y  y  each  into 


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^^tejmLiiiipTr '' 


STAIRS. 


123 


the  same  number  of  equal  parts  as  here  into  three. 
In  Fig.  3,  make  F  O  equal  to  one  third  of/  n,  and 
P  Q  equal  to  one  third  of  y  1/ ;  join  O  Q,  which  pro- 
duce to  meet  F  P  in  R.  Draw  R  M,  which  produce 
to  s.  La  R  s  take  any  point  m,  and  draw  m  f  per- 
pendicular to  R  s  ;  then,  parallel  to  R  s,  draw  A  a  s, 
B  b  r  t,  C  c  q  11,1)  dp  r,  E  e  0  iv,  Ffn  x. 

From  Fig.  4  transfer  the  heights  b  r,  c  q,  dp,  e  0, 
and  /  n,  to  the  corresponding  lines  b  r,  c  q,  dp,  e  o, 
f  n,  Fig.  3  ;  also,  from  Fig.  4  transfer  the  lines  a  s,rt, 
q  n,  p  V,  o  ic,  and  n  x,  to  a  s,  r  t,  q  v,  p  v,  0  ti',  and  n  x, 
Fig.  3 ;  then  through  the  points  11  o p  q  r  a  draw  a 
ctirve,  which  will  be  the  line  representing  the  under 
edge  of  the  inside  falling  mould  ;  also,  di-aw  the  curve 
X  IV  V  n  t  s,  which  is  the  line  representing  the  upper 
edge  of  the  same  falling  mould.  The  upper  and 
lower  edges  of  the  outside  falling  mould  will  thus 
be  found  —  N  being  the  centre  of  the  quadrants 
B  C  D  E  F  and  G  H  I  K  L;  draw  N  E  H,  N  D  I, 
N  C  K,  N  B  L,  cutting  the  convex  side  at  H,  I,  K ; 
and  draw  H  W,  I  V,  K  U,  L  T,  parallel  to  R  5 ;  and 
E  W,  D  V,  C  U,  B  T,  paraUel  to  /  m.  Also,  draw 
s  s,tt,  ti  n,  V  V,  parallel  to  /  m ;  and  make  1 1,  u  u,  v  v, 
respectively  equal  to  T  B,  U  C,  V  D ;  and  complete 
the  parallelogram  1 1,  s  s,  and  draw  the  curve  t  uv  3, 
which  will  meet  the  curve  s  t  u  v  tu  x  at  J,  the  point 
where  a  perpendicular  drawn  from  the  centre  N  of 
the  quadrant  meets  it.  In  the  same  manner,  find  the 
curve  nor;  and  we  shall  have  the  whole  projection 
of  the  helinet,  which  will  give  the  thickness  of  the 
stuff  reqrured  to  make  the  rail ;  by  drawing  a  straight 
line  iji  contact  with  two  points  on  the  under  side 
without  cutting  the  solid,  and  another  parallel  to  it 
from  the  point  X,  then  the  distance  between  these 
paraUel  lines  is  the  thickness  of  the  stuff. 

ON  THE  rORMATION   OF  THE  FALLING  MOULD. 

To  find  tlie  falling  mould  for  a  semicii'cular 
stair,  with  winders  round  the  semicii-cular 
part ;  or  the  falling  mould  for  a  semicu'cular 
staircase  level  roimd  the  semiciixle,  joined 
below  and  above  the  fliers. 

No.  1,  Fig.  1,  is  in  the  plan  of  the  rail  round  the 
circular  part,  and  of  a  small  portion  of  the  straight 
part  with  the  seats  or  plans  of  the  risers  round  the 
semicircular  part. 

Make  a  b,  No.  2,  equal  to  the  height  of  the  wind- 


ers; draw  a  c  and  b  d  at  right  angles  with  a  b;  make 
a  e  and  b  /each  equal  to  the  development  oi  I  p  or 
pm,  (No.  1 ; )  draw  e  I  and  d  k  parallel  to  a  b ;  make 
e  I  and  d  k  each  equal  to  the  height  of  a  step  ;  and 
join  e  g-  and  /  k.  This  description  so  far  applies  both 
to  Figs.  1  and  2. 

Li  Fig.  1,  No.  2,  join  c  f;  make  e  h  equal  to  e  g; 
and  /  i  equal  to  f  k,  and  draw  the  touching  curves 
g-r  h  and  i  s  k ;  and  g-  r  h  i  s  k  will  be  the  line  of  the 
rail. 

In  Fig.  2,  No.  2,  produce  g-  e  to  t,  and  k  f  to  u; 
bisect  a  b  at  s,  and  through  5  draw  t  u  parallel  to  a  c 
or  b  d;  from  g  t  cut  off  t  iv,  and  fi-om  u  k  cut  off  u  x, 
each  equal  to  g-  e  or  /  k  ;  and  describe  the  touching 
curves  g  z  s  and  5  y  x,  and  giv  z  s  y  xk  will  be  the 
line  of  rail. 

The  breadth  of  the  falling  mould  in  common  cases 
is  about  two  inches  ;  therefore,  di-aw  the  curve  lines 
each  at  an  inch  distance  from  the  line  of  the  rail,  and 
the  falling  mould  will  be  completed. 

Plate  S8. 

OX  THE  RESTING  POINTS. 
PROBLEM. 

To  find  the  position  of  the  plane  of  the  plank, 
and  the  resting  points,  so  that  the  thickness 
of  stuff  required  to  make  the  helinet  may  be 
the  least  possible. 

Fig.  1.  Let  abed  efg  h  be  the  plan  of  the  rail, 
of  which  the  part  b  c  d  efg  is  the  quadrant  of  a  cir- 
cle, and  the  part  a  b  g  h  of  a  rectangular  figure  ;  the 
straight  lines  a  b  and  A  g  being  tangents  to  the  outer 
and  inner  arcs  at  b  and  g,  and  the  circular  quadrants 
bed  and  g-  f  e  terminated  by  the  radii  b  I  and  g  I  ; 
then  suppose  two  equal  straight  lines,  one  erected 
upon  c  and  the  other  upon  /,  perpendicular  to  the 
plane  of  the  plan  of  the  rail,  and  let  c  Z  be  any  inter- 
mediate radius,  cutting  the  interior  quadrant  at  // 
produce  a  h  and  e  Ito  meet  each  other  in  k. 

Now,  if  a  straight  line  be  supposed  to  extend  from 
k  to  the  top  of  the  line  which  stands  upon  /,  the 
straight  line  thus  extended,  if  produced,  would  be 
higher  than  the  top  of  the  line  which  stands  upon  c  ; 
therefore,  if  a  plane  pass  through  a  k  and  through  the 
top  of  the  line  insisting  upon  /,  the  plane  will  pass 
above  the  top  of  the  line  standing  upon  c,  and  this 
will  be  the  case  with  every  section,  except  the  section 
b  g,  which  is  parallel  to  a  k;  therefore,  if  the  plane 


124 


STAIRS. 


of  the  plank  rest  upon  the  lower  section  a  h,  and  upon 

any  other  two  points  in  the  circular  part,  these  points 
must  be  in  the  concave  side ;  therefore,  in  this  case, 
the  resting  points  are  upon  /(,/,  e,  in  the  concave  side 
of  the  rail. 

Again :  in  Fig.  2,  let  I  c  and  a  6  be  produced  to 
meet  each  other  in  k ;  then  if  a  straight  line  be  ex- 
tended from  k  to  the  top  of  the  line  which  stands 
upon  c,  the  straight  line  thus  extended,  if  produced, 
would  be  higher  than  the  top  of  the  line  which  stands 
upon/;  therefore,  the  plane  which  passes  through  a  b, 
and  through  the  top  of  the  line  which  insists  upon  c, 
will  be  above  the  point  which  terminates  the  top  of 
the  line  insisting  upon  /;  whence  the  resting  points, 
a,  c,  cl,  are  all  upon  the  convex  side  of  the  rail. 

Lastly  :  in  Fig.  3,  if  a  plane  rests  upon  the  top  of 
the  two  lines  insisting  upon  c  and  /,  and  pass  through 
the  point  a,  —  and  if  a  line  be  supposed  to  stand  upon 
e,  perpendicular  to  the  plane  of  the  base,  of  such  a 
length  as  to  meet  the  plane  which  passes  through  a, 
and  through  the  upper  ends  of  the  lines  insisting 
upon  c  and  /,  —  it  is  evident  that  if  another  line  be 
supposed  to  be  erected  upon  d,  also  perpendicular  to 
the  plane  of  the  base  and  equal  in  height  to  the  line 
insisting  upon  e,  the  plane  wliich  passes  tlu'ough  the 
point  a,  and  through  the  tops  of  the  lines  insisting 
upon  c,f,  e,  must  be  above  the  top  of  the  line  insisting 
upon  d;  and  that  the  intersection  p  q  oi  the  plane 
passing  through  a,  and  the  points  in  the  line  insisting 
upon  c  and/,  must  be  parallel  to  c  /. 

It  is  now  evident  that  if  a  &  be  produced  to  r,  and  h  a 
to  5,  and  as  the  intersection  always  passes  tlirough  a, 
the  line  a  p  oi  the  intersection  of  the  plane  must  al- 
ways fall  withm  the  right  angle  r  a  s. 

It  is  likewise  evident,  if  the  resting  section  of  the 
rail  fall  between  c  /  and  a  h,  as  at  b  g,  the  middle 
resting  point  will  be  over  b  in  the  convex  side  of  the 
rail ;  and  if  the  resting  section  fall  between  c  /  and 
d  e,  the  resting  point  of  the  middle  section  must  be 
on  the  concave  side. 

SCHOLIUM  I. 
In  stairs  constructed  upon  the  letter  D  plan,  with 
winders  in  the  semicircular  part,  joined  to  a  series  of 
fliers  below  and  above,  where  the  winders  have  a 
higher  pitch  than  the  fliers,  the  first  two  resting 
points,  beginning  at  the  lowest  point,  will  be  on  the 
convex  side  of  the  rail,  while  that  at  the  highest  point 
is  on  the  concave  side. 


Fig.  4.  When  the  lower  line  of  heights  is  nothing, 
and  the  highest  double  to  the  middle  one,  the  line  of 
intersection  will  be  found  by  drawing  a  line  through 
the  seat  of  the  highest  and  middle  resting  point,  and 
producing  the  line  on  the  other  side  of  the  seat  of 
the  middle  resting  pomt,  until  the  part  produced  be 
equal  to  the  part  between  the  two  seats,  and  drawing 
a  line  through  the  lowest  point  a,  and  through  the 
extremity  of  the  point  thus  found ;  then  the  line  thus 
drawn  will  be  the  intersection. 

Thus,  in  the  present  case,  a  c  and  e  are  the  resting 
points  ;  join  c  c,  and  produce  e  c  to  A; ;  make  c  k  equal 
to  c  c,  and  join  a  k;  then  akis  the  intersection ;  and 
this  agrees  with  what  has  been  observed ;  for  if  a  k 
and  Z  c  be  produced,  they  will  meet  in  ?» ;  therefore,  / 
is  not  the  seat  of  the  resting  point :  if/  were  the  seat 
of  the  restmg  point,  maldng/  i  equal  to/  c,  and  join- 
ing a  i,  then  a  i  would  be  the  intersecting  line  ;  but  it 
is  not,  for  the  point  c  is  nearer  to  a  m  than  /. 

Corollary.  —  From  what  has  been  observed,  (see 
Fig.  5,)  that  the  intersecting  line  m  v  never  falls 
within  the  right  angle  at  o,  or  upon  the  plan  acdeh, 
therefore,  the  point  e  is  always  nearer  to  u  v  than  the 
point  d;  therefore,  the  point  e  is  the  seat  of  a  resting 
point. 

SCHOLIUM    II. 

Fig.  5.  From  the  same  given  heights,  and  from 
the  same  three  resting  sections  of  the  rail,  there  can- 
not be  more  than  four  intersecting  lines  by  maldng 
choice  of  one  resting  point  irom  each  section. 

For,  suppose  we  make  choice  of  the  points  d  and  c 
as  the  seats  of  the  resting  points,  and  join  the  line 
d  c,  and  produce  d  c,  suppose  to  some  imaginary  point 
X,  and  find  the  point  X  from  the  heights  upon  d  and 
c,  in  such  a  manner  that  the  line  thus  drawn  may 
not  cross  the  plan,  even  if  produced.  The  same 
thing  may  be  done  through  the  points  d  and  /,  also 
through  the  points  e  and  c,  and  through  the  pomts 
e  and  /;  then,  whichever  of  the  points,  d  or  e,  is  near- 
est to  the  intersecting  line  ?f  v,  that  point  is  the  seat 
of  the  resting  point. 

With  regard  to  the  ratio  between  the  whole  line 
drawn  through  the  seats  of  the  resting  points  and 
the  part  of  it  between  the  said  seats,  it  is  the  same 
as  the  ratio  between  the  highest  line  and  the  line 
insisting  on  the  seat  of  the  middle  section. 

Suppose  (in  Fig.  5)  the  seats  of  the  resting  points 
are  c  and  r;  join  c  c,  and  produce  it  to  i;  draw  e  I 
and  c  k  perpendicular  to  e  i;  make  e  I  equal  to  the 


SlriJ.3  P' 


n  1)11 


\:- 


F{^,2. 


I'  t  i  3  V 


S.Ii.ll 


,''1  'III 


STAIRS. 


125 


height  insisting  upon  e,  and  c  k  equal  to  the  height 
insisting  upon  c ;  join  Ik, and  produce  it  to  i.  Then, 
because  of  the  similar  triangles  e  i  I  and  c  i  k,  i  e  : 
i  c  :  :  e  I :  ck;  that  is,  i  c  is  the  same  part  of  i  e  that 
c  A;  is  of  e  I;  therefore,  if  e  /  be  double  of  c  k,  e  i  will 
be  double  of  c  i,  or  i  c  will  be  equal  to  c  e. 

If  the  workman  should  not  understand  the  demon- 
stration now  given,  he  may  proceed  mechanically 
thus,  the  seats  of  the  resting  points  being  a,  c,  e. 

Join  e  c,  and  produce  ecioi ;  draw  e  I  and  c  k  per- 
pendicular to  i  e ;  make  e  I  equal  to  the  height  upon 
e,  c  k  equal  the  height  upon  c ;  join  I  k  and  produce 
it  to  /,  and  join  i  a;  then  i  a  is  the  intersecting  line. 
Produce  i  a  both  ways  to  ti  and  v,  cf  to  o  and  i',  and 
d  e  to  o  and  m;  di-aw  d  r,  e  m,  and  o  q  perpendicular 
to  du;  draw  o  p,  fia,  and  c  n  perpendicular  to  o  v; 
make  c  n  equal  to  c  k,  and  join  v  n;  produce  v  nto 
p ;  mak  o  q  equal  to  o  p,  and  e  m  equal  to  e  I;  join 
m  q ;  then,  if  m  g  be  produced,  it  will  meet  uv  in  ii. 
This  may  easily  be  conceived  by  raising  the  triangles 
i  e  I,  V  0  p,  and  u  e  m,  upon  their  bases,  i  e,  v  c,  and 
d  u ;  then  c  k  will  coincide  with  c  n,  e  I  with  e  m, 
and  o  p  with  o  q ;  and  the  lines  i  1,  v  p,  and  r  u  will 
all  be  in  the  inclined  plane  of  which  its  intersection 
is  u  V. 

COXSTRTJCTION  OF  THE  FACE  MOULD. 

Fig.  7.  Let  a  d  e  f  g  h  i  be  the  plan  of  the  rail,  ef 
g  h  a  portion  of  the  straight  part,  i  being  the  upper, 
and/ the  lower,  resting  points.  But  as  the  place  of 
the  middle  resting  point  d  vrSi.  affect  the  tliickjiiess  of 
the  stuff,  it  ought  not  to  be  arbitrarily  assumed  j 
though  it  would  be  diiScult  to  show  upon  any  prin- 
ciple where  it  should  be  exactly.  It  is,  however, 
ascertained  by  trial  that  its  position  may  vary  to  a 
considerable  distance  without  affecting  the  thickness 
of  the  stuiT  hi  any  great  degree  ;  and  as  experiment 
shows  that  it  is  nearly  in  the  middle  of  the  develop- 
ment of  a  d  ef,  it  is  here  taken  in  the  middle,  so  that 
the  stretch-out  of  ad  may  be  equal  to  the  stretch-out 
of  df. 

Figs.  6  and  7.  In  the  figure  of  the  falling  mould, 
produce  the  base  a  e  of  the  winders  to  /,  then  a  e 
(Fig.  6)  bemg  equal  to  the  development  of  a  e,  (Fig. 
7,)  make  a  d  (6)  equal  to  the  development  of  ad,  (7,) 
and  make  e  f  (6)  equal  to  e  f,  (7  ;)  draw  / 1  parallel 
to  a  b,  (6,)  cutting  the  upper  side  of  the  falling  mould 
at  1,  (6 ;)  parallel  to/a  draw  I  i,  cutting  a  b  at  i,  (6  ;) 
in  i  I  make  i  d  (6)  equal  to  i  d,  (7 ;)  draw  d  m  (6)  par- 


allel to  a  b,  cutting  the  upper  side  of  the  falling 
mould  at  m ;  draw  vi  n  parallel  to  /  a,  cutting  a  6  at 
n ;  draw  d  r  parallel  to  a  b,  cutting  m  n  at  /•,  (G.) 

Join  o  r,  and  produce  it  to  meet  i  I  at  q ;  make  i  q 
(7)  equal  to  iq,  (6;)  join/ 7,  (7,)  and  produce  f  q  to 
k  i.  Through  g  draw  k  I  perpendicular  to  k  q. 
Through  i  draw  i  z  parallel  to  k  q,  cutting  k  I  at  z. 
Make  z  z  equal  to  io,  (6  ;)  and  join  k  z,  (7,)  and  pro- 
duce k  z  tx)  I :  draw  a  I  parallel  to  z  z. 

TO  FI>rD  THE  FACE  MOTJLD. 

Fig.  7.  Draw  I  a  and  z  b  perpendicular  to  kl; 
make  I  a  equal  to  I  a,  z  i  equal  to  z  i,  and  join  i  a; 
then  i  a  will  form  the  part  of  the  face  mould  repre- 
sented by  i  a  on  the  plan.  Draw  k  f  perpendicular 
to  k  I,  and  make  kf  equal  to  kf.  Draw  g  g  parallel 
to  z  z,  cutting  k  I  2A,  g,  and  join  gf.  Again  :  draw 
h  u  parallel  to  z  z,  cutting  k  I  at  u  and  k  I  at  tt. 
Draw  w  h  perpendicular  to  k  I,  and  make  u  h  equal  to 
uh;  draw  h  e  parallel  to  gf,  and/  e  parallel  to  g  h ; 
then  e  f  g  h  will  form  the  part  of  the  face  mould 
corresponding  to  the  straight  part  e  f  gh, in  the  plan. 
The  intermediate  points  of  the  face  mould,  which 
form  curves  of  the  outside  and  inside  of  the  rail,  are 
thus  found.  Through  any  pomt  c,  in  the  convex  side 
of  the  plan,  draw  c  y  parallel  to  z  z,  cutting  k  I  at 
y  i,  and  k  I  at  y,  and  the  concave  side  of  the  plan  at  t. 
Draw  y  c  perpendicular  to  k  I,  and  in  y  c  make  y  t 
equal  to  y  t,  and  y  c  equal  to  y  c ;  then  tis  a.  point  in 
the  concave  side,  and  c  a  point  in  the  convex  side,  of 
the  face  mould.  A  sufficient  number  of  points  being 
thus  found,  the  curved  parts  of  the  face  mould  may 
be  drawn  by  hand,  or  by  a  sfip  of  wood  bent  to  the 
curve. 

It  will  be  perceived  that  I  have  been  obfiged,  in 
some  instances,  to  use  the  same  letter  of  reference 
t«'ice ;  but  they  are  so  placed,  that  the  one  referred 
to  can  be  ascertained  without  any  difficulty. 

Plates   89  &  90. 

REdPROCAL  SPIRAL  AND   SCROLL. 

To  draw  the  reciprocal  spiral  for  a  scroll. 

Suppose  the  ordinate  0  q  (Fig.  1)  to  be  given. 
Make  a  b  (Fig.  2)  equal  to  0  q,  and  through  b  draw 
c  d,  making  an  angle  with  ab ;  then  take  &  c  in  a 
greater  or  less  ratio  to  6 1,  as  a  less  or  greater  part  of 
the  scroll  is  wanted,  or  as  the  scroll  is  required  to 


126 


STAIRS. 


have  a  flatter  or  qmcker  curve  at  the  remote  extrem- 
ity ;  for  instance,  b  c  in  this  example  is  double  to  b  1. 

Suppose  the  point  c  to  be  now  fixed ;  draw  c  e 
parallel  to  a  b,  and  a  e  parallel  to  c  d;  make  1,  2; 
2,  3 ;  3,  4 ;  &c.,  each  equal  to  b  1,  and  draw  the  lines 
1  e,  2  e,  3  e,  4  e,  &c.,  cutting  a  b  respectively  at 
e/g",  &c. 

Li  Fig.  1,  divide  the  space  round  the  centre  o  into 
eight  equal  angles,  which  will  be  easily  done  by 
drawing  a  circle  through  q,  and  dividing  the  circum- 
ference into  eight  equal  parts,  beginning  at  q  ;  draw 
the  portions  o  p,  o  q,  o  r,  o  s,  &c.  Make  o  p  (Fig.  1) 
equal  to  twice  a  b,  (Fig.  2;)oq  (Fig.  1)  is  equal  to 
a  b,  (Fig.  2;)  also,  make  o  r,  o  s,  of,  &c.,  (Fig.  1,) 
respectively  equal  to  a  e,  a  f,  a  g,  &c.,  (Fig.  2.) 
Through  all  the  points  p  q  r  s  t,  &c.,  draw  the  curve 
p  q  r  s  t,  &c.,  which  will  be  the  spiral  required. 

For  want  of  room,  a  b  (Fig.  2)  is  only  made  equal 
to  half  the  length  it  ought  to  have  been ;  for  a  &  wiU 
be  divided  into  parts  of  the  same  length,  whether  a  b 
is  double  and  b  c  equal  to  b  1,  or  a  b  as  it  is,  and  b  c 
double  of  &  1. 

SCHOLIUM. 

This  spiral  is  well  adapted  to  the  purpose  of  hand 
railing,  for  it  may  be  made  close  or  to  extend  at 
pleasure,  as  may  be  seen  by  the  subsequent  examples. 

This  spiral  may  be  extended  so  as  to  form  the  rail 
itself  by  a  gentle  curve,  which  will  approach  nearer 
to  a  straight  line  the  more  it  is  extended.  The  forms 
of  stairs  attached  to  pulpits  are  often  very  fanciful ; 
thek  plan  requires  to  be  formed  in  the  most  graceful 
manner  ;  the  reciprocal  spiral  may  be  applied  to  this 
purpose  with  advantage,  as  the  effect  produced  will 
be  both  beautiful  and  elegant.  It  may  also  be  ap- 
plied to  form  the  plan  of  the  riser  of  the  curtail  step 
into  a  gentle  curve,  which  will  be  in  perfect  unison 
with  the  scroll  itself.  The  plans  of  the  other  steps 
may  be  formed  to  the  same  curve ;  but  the  curvature 
may  be  made  less  in  each,  as  the  other  risers  recede 
from  that  of  the  curtail  step,  till  at  last  the  risers  be- 
come straight.  The  property  of  this  scroll  may  be 
shown  arithmetically,  thus :  let  any  given  radius  be 
called  unity,  or  one,  and  let  this  radius,  so  called,  be 
the  gi-catest  radius ;  let  «  be  any  constant  number, 
which  must  be  in  the  same  scroll,  but  variable  in 
difTcrent  scrolls,  and  let  a;  be  a  variable  number  in  the 
same  scroll,  then  will  j^_  represent  any  ordinate ;  thus 
the  first,  second,  third,  &c.,  ordinates,  by  making  x 


respectively  0,  1,  2,  3,  &c.,  will  be  respectively 


By  giving  n  a  value,  the  form  of  the 
determined.     Thus,  make  71  =  2,  and 


_!! ^  &c 

scroll  will  be 
we  shall  have  the  series  of  ordinates,  |,  f ,  f ,  f ,  |,  &c. 
This  will  give  the  scroll  Fig.  1,  plate  91. 


Make  n^A:  then 


-XI,  4t;,  -^,,&c.  will  become 

n-f-  1'  n  +  2'  n-j- J' 


f )  &)  I)  t,  &c.,  respectively.  These  are  the  respective 
ratios  of  the  ordinates  o  a,  o  b,o  c,o  d,o  e,  Sec,  Fig.  1, 
plate  88. 

Lastly :  make  n  =  8;  then  ;,  „-^,  ~,  ;^,&c.,wm 
become  f ,  |,  j?^^,  /j,  &c.,  respectively.  These  are  the 
respective  ratios  of  the  ordinates  oa,  o  b,  o  c,  o  d,  &c.. 
Fig.  3,  plate  88. 

So  that  we  have  both  a  geometrical  and  an  arith- 
metical rule  for  drawing  the  reciprocal  spiral. 

It  may  be  here  observed  that  this  spiral  is  the  only 
one  that  can  be  employed  in  forming  the  volutes  of 
the  Corinthian  capital. 

Fig.  3,  plate  90,  exhibits  the  scroll  with  the  scale 
drawn  on  the  first  radius. 

Plate  91. 

To  describe  the  face  and  falling  mould  for  pre- 
paring the  scroll. 

Let  a  b  he  the  first  quarter  of  the  scroll,  c  the  cen- 
tre ;  draw  d  e  parallel  to  b  c,  touching  the  outer  spiral 
at  d ;  draw  e  G  parallel  to  c  a,  and  through  a  draw 
F  G  parallel  to  c  b ;  make  G  F  equal  to  the  breadth 
of  a  step ;  di-aw  F  H  perpendicular  to  G  H ;  make 
F  H  equal  to  the  height  of  a  step,  and  join  H  G ; 
then  G  H  is  the  pitch  line  of  the  stair.  Draw  lines 
parallel  to  a  c,  cutting  the  inner  edge  of  the  scroll  at 
the  points  /,  g;  h,  the  outer  edge  at  i,  k,  I,  m,  n,  the 
straight  line  F  G  in  the  points  n,  o,  p,  q,  r,  and  H  G 
at  the  points  N,  O,  P,  Q,  R ;  let  a  c  cut  the  concave 
side  of  the  scroll  at  t,  and  let  it  be  produced  to  cut 
H  G  at  A ;  from  the  point  //,  where  the  line  d  c  cuts 
the  concave  spiral  of  the  scroll,  draw  h  W  parallel 
to  a  c,  cutting  A  G  at  W,  F  G  at  r,  and  the  con- 
vex spiral  at  ?/.  Draw  W  H  and  G  E  perpendicular 
to  II  G. 

Make  W  H  and  G  E  each  equal  to  v  h  or  G  e, 
and  join  H  E ;  through  the  points  N,  O,  P,  Q,  R, 
draw  lines  perpendicidar  to  H  G  ;  in  the  perpendicu- 
lars make  AT,  N  F,  O  G,  each  respectively  equal 
to  a,  t,  n,  f,  o,g;  also,  make  N  I,  O  K,  P  L,  Q,  M, 
R  N,  each  respectively  to  «  i,  0  k,  p  1,  q  m,  r  n ;  draw 
T  X  paraUel  to  H  G,  and  draw  the  curves  T  F  G  H 


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127 


and  A  I  K  L  M  N  E,  which  will  complete  the  face 
mould  for  the  twisted  part  of  the  scroll,  which  is  to 
be  glued  to  the  other  part  formed  in  one  level  piece. 
The  falling  mould  is  constructed  as  follows :  Fig.  2. 
Let  F  G  H  be  the  pitch  board,  as  in  Fig.  1.  Divide 
F  G  into  eight  equal  parts,  and  make  F  a  equal  to 
three  of  the  parts  ;  through  a  di'aw  d  q  perpendicular 
to  F  G,  cutting  H  G  at  ^ ;  produce  H  G  io  d;  draw 
any  line  q  s  parallel  to  F  G,  and  make  q  s  equal  to 
the  sti'ctcli  out  of  the  first  two  quarters,  a,  b,  v,  of  the 
outward  spiral.  Fig.  1 ;  through  s  draw  u  d  parallel 
to  H  F ;  in  H  d  take  any  distance  d  b,  and  draw  b  a 
parallel  to  F  G,  cutting  u  d  at  a.  Again :  in  H  d 
take  b  c  equal  to  b  a,  and  join  c  a;  through  ^j  draw 
p  t  parallel  to  c  a,  cutting  n  b  in  t ;  draw  t  v  parallel 
to  F  G,  cutting  H  fZ  at  w ;  then  will  v  t  ha  equal  to 

V  p;  divide  v  p  and  v  t  each  into  the  same  number 
of  equal  parts,  and  draw  the  intersecting  lines  to  the 
points  of  division,  and  the  curves  formed  will  be  the 
upper  edge  of  the  falling  mould ;  the  other  edge  will 
be  formed  by  gauging  off  the  thickness  of  the  rail. 

Plate  92. 

APPLICATION  OF  THE  FACE  MOULD  TO  THE  PLANK. 

To  form  the  figure  of  tlie  face  mould  upon  each 
side  of  the  plank,  so  that,  when  the  super- 
fluous wood  is  cut  away,  the  carved  surfaces 
formed  thereby  may  stand  perpendicular  to 
the  plan,  supposing  the  piece  thus  formed  set 
in  due  position. 

Let  abed  e  f  g  be  the  Fig.  1  of  the  face  mould, 
placed  in  due  position  to  the  pitch  line  g  i,  as  when 
traced  from  the  plan  ;  and  let  Fig.  2  represent  a  de- 
velopment of  the  plank  where  X  represents  the  top, 

Y  the  edge,  and  Z  the  under  side  of  the  plank. 

The  face  mould  is  first  applied  to  the  top  X,  so 
that  the  points  g  and  the  chord  line  g  e  oi  the  mould 
may  make  the  same  angle  at  g  with  the  arris  line  g  e 
of  the  plank  that  the  figure  of  the  mould  at  Fig.  1 
makes  with  the  pitch  line ;  di-aw  g  K,  making  the 
same  angle  with  i  g  that  the  pitch  line  makes  with 
any  connecting  line  or  perpendicular,  and  draw  the 
figure  of  the  mould  on  the  plank ;  apply  the  same 
mould  to  the  other  side  Z  of  the  plank  to  the  point 
K,  so  that  the  chord  may  make  the  same  angle  with 
the  other  arris  as  on  the  first  side,  and  draw  the  fig- 
ure of  the  mould  on  this  last  side ;  then  the  soUd 


which  is  formed  by  cutting  away  the  superfluous 
wood  is  the  piece  required. 

But  as  it  may  be  desirable  to  apply  the  tips  of  the 
mould  g  and  e  close  to  the  edge  of  the  plank.  Fig.  3 
shows  how  the  plank  is  to  be  lined  out  according  to 
this  application.  Here  the  pitch  line  g  K  makes  the 
same  angle  with  the  upper  arris  of  the  plank  as  be- 
fore ;  di-aw  g  L  perpendicular  to  either  arris,  cutting 
the  lower  arris  at  L ;  make  the  angle  K  L  G  equal 
to  the  angle  e  g  i,  Fig.  1 ;  make  L  g  equal  to  L  K, 
and  draw  the  chord  g"  e,  in  the  plane  Z,  parallel  to 
the  arris  line ;  in  the  plane  Z  apply  the  tips  g  and  e 
of  the  face  mould  to  the  line  g  e,  as  exhibited  in  the 
figure ;  then  draw  the  form  of  the  face  mould  as  before. 

DEMONSTRATION. 

Fig.  2.  Draw  g  L  in  the  plane  Y,  cutting  the  lower 
arris  of  the  plank  at  L  ;  draw  the  ciiord  K  e  of  the 
face  mould  in  the  plane  Z,  and  draw  L  M  in  the  same 
plane  parallel  to  K  e ;  also  draw  L  s  perpendicular 
to  K  e,  cutting  K  e  at  s.  Now,  imagine  the  figure 
M  L  K  e  to  be  moved  so  as  to  revolve  on  the  point 
L,  until  L  M  come  into  the  arris  L  m;  it  is  evident 
that  the  point  K  will  move  in  the  circumference  of 
the  circle  K  k,  and  wiU  come  into  the  position  k ;  and 
that  the  angle  K  L  A*  will  be  equal  to  the  angle  »i  L  M ; 
but  the  angle  7ii  L  M  is  equal  to  the  angle  agi,  Fig.  1. 
Again  :  reverting  to  Figs.  2  and  3,  it  is  plain  in  Fig.  3, 
that  if  the  angle  KTi  g  in  the  plane  Z  be  made  equal 
to  the  angle  e  g  i,  Fig.  1,  and  if  L  g-  be  made  equal 
to  L  K,  and  the  mould  applied  to  each  side  of  the 
plank  as  in  the  figure,  the  solid,  when  cut  out,  by 
taking  away  the  superfluous  wood,  will  be  equal  and 
similar  in  all  its  corresponding  parts  to  that  cut  out 
according  to  the  oblique  chords.  Fig.  2. 

Fig.  4  shows  another  application  where  the  chord 
of  the  face  mould  is  neither  applied  to  the  angle  e  g  i, 
nor  paraUel  to  the  arris  lines ;  but  as  this  application 
is  rather  curious  than  useful,  the  bare  inspection  of 
the  diagram  wiU  render  it  sufficiently  clear  to  those 
who  will  take  the  trouble  to  consider  it. 

Plate  93. 

ON  THE  FORMATION  OF  THE  STRING. 
PROBLEM. 

To  form  the  soffit  of  a  stair  with  easings  at  the 
junctions  of  the  fliers  and  winders. 

Let  Fig.  1  be  the  plan  of  the  staur,  the  breadth  of 


128 


STAIRS. 


the  steps  being  divided  equally  along  the  middle 
line.  Suppose  the  winders  to  begin  at  riser  C,  and 
let  the  string  from  the  riser  of  the  curtail  step  to  the 
point  C  be  straight. 

The  first  thing  to  be  done  is  to  stretch  out  the 
string;  but  in  this  development  it  will  not  be  neces- 
sary to  exhibit  it  entirely,  the  circular  part  and  a  small 
portion  of  the  straight  part  at  each  end  will  be  suffi- 
cient; therefore,  beginning  at  A,  we  shall  take  in  the 
two  fliers  over  A  B  and  B  C. 

In  Fig.  2,  draw;?  I  parallel  to  the  rail,  and  makep  I 
equal  to  the  length  of  tlie  line  abed  e  f  g  h.  Draw 
I  K  perpendicular  to  p  I,  make  1 1 ;  1,  2 ;  2,  3 ;  equal 
to  tlie  heights  of  the  three  risers  over  ABC,  Fig.  1 ; 
also,  in  Fig.  2,  make  3,  4 ;  4,  5 ;  5,  6 ;  6,7;  7,  8 ; 
each  equal  to  the  height  of  the  winders  over  D,  E,  F, 
G,  H.  h\  the  plan  Fig.  1,  suppose  a  line  drawn  tlirough 
the  centre  x  perpendicular  to  the  rail,  cutting  the  mid- 
dle line  at  D,  and  let  this  line  be  produced  to  ?;,  Fig.  2 ; 
in  Fig.  2,  draw  3  c  parallel  to  p  I,  cutting  xuatu; 
join  up  and  m  7  ;  draw^j  a  in  the  same  straight  line 
with  the  riser  A,  b  b  in  the  same  straight  line  with 
the  riser  B,  and  c  c  in  the  same  straight  line  with  the 
riser  C,  to  cut  p  ti  at  b  and  q  ;  make  ti  r  equal  to  u  q, 
then  form  the  easing  curve  q  r ;  draw  2  c,  i  d,  5  c, 
€/,  7  g;  parallel  to^  I,  cutting  the  easing  curve  at  d 
and  e,  and  m  7  at  /  and  g ;  draw  d  d,  e  e,  f  f,  g  g^ 
parallel  to  I  K ;  make  c  d  equal  to  c  d,  d  e  equal  to 
d  e,  e/ equal  to  ef,  fg  equal  to  fg,  and  g  h  equal 
to  g  h;  then  D  H  being  divided  into  equal  parts  at 
the  points  E,  F,  G,  join  D  d,  E  e,  F/,  G  g-,  and  pro- 
duce them  to  the  wall  line ;  in  Fig.  2,  draw  the  curve 
P  Q,  R  parallel  to  p  q  r  zt  a  proper  distance,  which 
completes  one  half  of  the  string.  The  manner  of 
completing  the  other  half  is  evident. 

OBSERVATIONS. 

Having  given  the  details  of  finishing,  I  shall  now 
proceed  to  offer  a  few  general  remarks  in  relation  to 
this  subject. 

The  selecting  of  biiilding  materials  has  not,  in  gen- 
eral, received  that  care  and  attention  wliich  this  im- 
portant subject  demands.  Many  buildings  have  been 
ruined,  the  owners  of  others  have  been  displeased, 
and  not  without  just  cause  ;  and  the  workman  has  lost 
his  reputation,  and  forfeited  his  claim  to  public  patron- 
age, solely  firom  neglect  in  this  important  particidar. 

The  first  care  of  a  master  builder  should  be  to  see 
that  his  lumber  is  properly  seasoned.  The  best 
method  of  seasoning  is,  after  boards  or  plank  have 


been  sawed  at  the  mills,  they  should  be  immersed  in 
salt  or  fresh  water  for  the  space  of  one  or  two  months ; 
larger  lumber  should  remain  in  this  situation  till  the 
sap  is  properly  extracted  from  tlie  wood ;  this  opera- 
tion preserves  the  lumber  in  some  degree  fi-om  the 
dry  rot.  Next  take  the  boards  or  plank  out  of  the 
water,  and  pile  them  in  a  situation  where  the  air 
may  have  a  free  circulation  through  and  on  all  sides 
of  the  piles.  They  should  remain  in  this  situation 
for  one  year ;  then  take  them  down  and  select  such 
as  are  suitable  for  finishing :  these  should  again  be 
stuck  in  a  buUding,  or  covered  in  such  a  manner  as 
to  be  secure  from  the  weather ;  they  should  remain 
in  this  situation  at  least  sLx  months  before  they  are 
used.  While  preparing  the  stuff  for  finishing,  it 
should  be  spread  to  the  sun  every  fair  day,  and  put 
under  cover  at  night  for  three  or  four  weeks  before  it 
is  put  together.  The  mechanic  will  feel  himself  well 
paid  for  his  time  and  trouble  when  he  shall  examine 
his  work  at  any  subsequent  period. 

Framing  timber  should  be  squared  up  soon  after 
being  taken  out  of  the  water,  and  stuck  up  under 
cover  for  the  space  of  six  months  before  it  is  worked 
into  buUdings ;  this  wUl  correct  the  erroneous  idea, 
in  many  cases,  where  the  settling  of  the  floor  has  been 
attributed  to  bad  workmanship,  when,  in  fact,  it  has 
been  occasioned  by  the  shrinking  of  the  timber. 

The  Idnd  of  lumber  in  general  use  for  building  in 
the  New  England  States  is  white,  yellow,  pitch,  and 
Norway  pine ;  spruce,  cedar,  and  sometimes  hemlock, 
white  and  basswood.  The  hard  woods  are  oak,  ma- 
hogany, maple,  cherry,  and  ash.  In  the  Southern 
States  there  is  found  a  superior  species  of  pine,  which, 
for  durability,  is  preferable  to  northern  pine,  when 
used  for  floor  boards  or  joists. 

Pine  boards  and  joists  are  sorted  into  different 
qualities,  known  as  Nos.  1,  2,  and  3.  No.  1  is  square 
edged,  free  from  knots,  shakes,  and  rot.  No.  2,  the 
second  quality,  is  sound,  not  entirely  free  from  knots, 
and  is  square  edged.  No.  3  has  Imots,  shakes,  is  wane 
edged,  and  has  some  rot.  No.  1  is  used  for  the  best 
of  finishing ;  No.  2  for  rough  boarding,  such  as  roofs, 
side  and  end  boarding,  &:c.,  where  the  edges  are  re- 
quired to  be  tongucd  and  grooved,  or  rabbeted.  From 
this  quality,  by  properly  sorting  them,  good  floor 
boards  may  be  selected,  which  should  be  sawed  from 
four  to  seven  inches  wide ;  many  of  them  will  be 
clear,  and,  after  they  arc  A^TOught  to  a  thickness,  the 
clearest  may  be  used  for  the  best  rooms,  and  the  others 
as  they  may  be  suitable  for  the  different  rooms. 


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BRIDGES. 


129 


BRIDGES. 


Mr.  Ithiel  To\vn's  improvement  in  the  construction  of  bridges 
being  considered  preferable  to  any  mode  of  bridge  building  yet  laid 
before  the  public,  it  has  been  thought  best,  in  this  department  of  the 
work,  to  give  his  arguments  and  description  in  his  own  words,  and 
to  refer  the  reader  to  the  introduction  for  such  additional  facts  and 
remarks  as  has  been  thought  necessary  to  lay  before  him,  in  order 
to  give  him  a  more  perfect  understanding  of  this  important  branch 
of  his  profession. 


Plate   94 

A  Description  of  Ithiel  Toioi's  Improvement  in  the 
Construction  of  icooden  and  iron  Bridges.,  intended 
as  a  general  System  of  Bridge  Building  for  Rivers, 
Creeks,  and  Harbors,  of  whatever  Kind  of  Bottoms, 
and  for  ani/  practicable  Width  of  Span  or  Opening, 
in  every  Part  of  the  Country. 

To  establish  a  general  mode  of  constructing 
wooden  and  iron  bridges,  and  which  mode  of  con- 
struction shall,  at  the  same  time,  be  the  most  simple, 
permanent,  and  economical,  both  in  erecting  and 
repairing,  has  been  for  a  long  time  a  desideratum  of 
great  importance  to  a  country  so  extensive,  and  in- 
terspersed with  so  many  wild  and  majestic  rivers  as 
ours  is.  It  has  been  too  much  the  custom  for  archi- 
tects and  builders  to  pUe  together  materials,  each 
according  to  his  own  ideas  of  the  scientific  principles 
and  practice  of  bridge  building,  and  the  result  has 
been,  first,  that  nearly  as  many  modes  of  construc- 
tion have  becH  adopted  as  there  have  been  bridges 
built ;  second,  that  many  have  answered  no  purpose 
at  all,  and  others  but  very  poorly  and  for  a  short  time  ; 
while  most  of  the  best  ones  have  cost  a  sura  which 
deters  and  puts  it  out  of  the  power  of  probably  five 
sixths  of  those  interested  in  ferries  to  substitute 
bridges  which  would  obviate  the  many  dangers  and 
delays  incident  to  them. 

That  architects  and  builders  adhere  to  their  own 
ideas  in  the  construction  not  only  of  bridges,  but  of 
buildings,  is  most  universally  true.  They  are  obsti- 
nately opposed  to  the  adoption  of  any  other  mode 
than  their  own ;  consequently  it  is  true,  and  it  is 
seen  to  be  so  throughout  the  country,  (and  it  is  much 
to  be  regretted,)  that  in  very  few  instances,  either  in 
erecting  bridges   or  buildings,  there  is   any   model, 

17 


either  uniform  or  in  genera!,  very  good.  But  in 
bridges  and  public  buildings,  it  would  .seem  some- 
thing better  might  be  expected  if  men  scientifically 
and  practically  acquainted  with  such  subject.s  would 
step  forward  in  a  disinterested  manner,  and  deter- 
mine between  principles  which  arc  philosophical  and 
those  which  ase  not,  and  between  modes  of  execution 
which  are  founded  in  practice  and  experience  and 
those  which  are  founded  in  ignorance  and  inexperi- 
ence ;  and  in  matters  of  taste,  if  they  would  deter- 
mine in  favor  of  classic  and  well-established  usage, 
and  not  that  which  is  the  offspring  of  unimproved 
minds  and  whimsical  fancies,  which  are  ever  upon  the 
rack  to  establish  new  things  —  the  creation  of  their 
own  imaginations,  and  which  are,  therefore,  sure  to 
be  wrong,  for  this  good  reason  —  that  their  authors 
are  so. 

Perhaps  the  following  propoeition  comprises  what 
is  the  most  important  to  be  determined  with  regard 
to  a  general  system  of  bridge  building,  viz. :  — 

By  what  construction  or  arrangement  will  the 
least  quantity  of  materials  and  cost  of  labor  erect  a 
bridge  of  any  practicable  span  or  opening  between 
piers  or  abutments,  to  be  the  strongest  and  most  per- 
manent, and  to  admit  of  the  easiest  repair. 

In  giving  the  best  answer  to  this  proposition 
which  I  am  capable  of  after  a  number  of  years' 
attention  to  the  theory  and  practice  of  this  subject,  I 
shall  refer  to  plate  94.  The  mode  of  construction  is 
so  simple  and  plain  to  inspection  as  to  require  little 
explanation  of  it. 

Fig.  3  is  an  elevation  of  one  of  the  trusses  of  a 
bridge ;  one,  two,  or  three  of  those  trusses  placed 
vertically  upon  piers  are  to  be  considered  as  the  sup- 
port of  the  bridge,  and  are  to  be  of  a  height,  at  least, 
sufficient  to  admit  a  wagon  to  pass  under  the  upper 
beams  which  lie  horizontally  upon  the  top  string 
piece  of  the  side  trusses ;  and  on  these  same  side 
string  pieces  rest  the  feet  of  rafters,  which  form  a 
roof  to  shingle  upon.  In  this  case  a  middle  truss  is 
used,  which  will  always  be  necessary  in  bridges  of 
considerable  width.  The  height  of  it  wiU  be  as 
much  greater  than  the  side  ones  as  the  height  or 
pitch  of  the  roof.     The  height  of  the  trusses  must 


130 


BRIDGES. 


be  equal  to  the  whole  height  of  the  bridge  required, 
and  is  to  be  an  exact  continuation  of  the  work 
represented  in  Fig.  1. 

The  height  of  the  trusses  is  to  be  proportioned  to 
the  width  of  the  openings  between  the  piers  or 
abutments,  and  may  be  about  one  tenth  of  the  open- 
ings, when  the  piers  arc  fifteen  feet  or  more  apart  — 
a  less  span  requiring  about  the  same  height,  for  the 
reasons  before  stated. 

The  diagonal  bearing  of  these  trusses  is  composed 
of  sawed  plank,  ten  or  eleven  inches  wide,  and  from 
three  to  three  and  a  half  inches  thick.  It  may  be 
sawed  from  any  timber  that  will  last  well  when  kept 
dry.  White  pine  and  spruce  are  probably  the  best 
kinds  of  timber  for  the  purpose,  on  account  of  their 
lightness,  and  their  not  being  so  subject  to  spring  or 
warp  as  white  oak. 

The  nearer  those  braces  are  placed  to  each  other, 
the  more  strength  will  the  truss  have,  and  in  no  case 
are  they  to  be  halved  or  gained  where  they  intersect 
each  other ;  but  they  are  to  stand  in  close  contact, 
depending  entirely  on  three  or  four  trunnels  which 
go  through  each  joint  or  intersection;  and  where  the 
string  pieces  pass  over  these  joints,  the  trunnels  go 
through  them  also,  and  are  each  of  them  wedged  at 
each  end  to  keep  the  timber  in  close  contact.  A 
chain  or  clamp  is  necessary  to  bring  the  work  tight 
together. 

Trunnels  may  be  made  of  white  oak,  one  and  a 
half  inches  in  diameter.  They  are  made  very  cheaply 
and  excellently  by  being  rived  out  square,  and  driven, 
while  green  or  wet,  through  a  tube  fitted  to  a  block, 
and  ground  to  an  edge  at  the  top  end.  They  are 
then  to  be  seasoned  before  they  are  used. 

The  string  pieces  arc  composed  of  two  thicknesses 
of  plank,  of  about  the  same  dimensions  as  the 
braces,  and  they  arc  so  put  together  as  to  break 
joints,  as  shown  at  Fig.  4.  This  renders  long-hewn 
timber  iinnecessary,  as  also  any  labor  in  making 
splices  and  putting  on  iron  work. 

For  any  span  or  opening  not  exceeding  one  hun- 
dred and  thirty  feet,  one  string  piece  at  top  and  one 
at  bottom  of  each  truss,  if  of  a  good  proportion  and 
well  secured,  will  be  sufTicicnt ;  but  as  the  span  is 
extended  beyond  one  hundred  and  thirty  feet,  two  or 
more  at  top  and  bottom  would  be  required,  as  shown 
in  Fig.  1,  where  two  string  pieces  run  over  the  two 
upper  and  lower  series  of  joists  or  intersections  of  the 
braces :  and  in  wide  spans  the  floor  beams  may  be 


placed   on    the   second    string    piece,  as   shown   at 

Fig.  1. 

Fig.  5  shows,  on  a  larger  scale,  how  each  joint  is 
secured,  by  which  it  is  seen  that  the  trunnels  take 
hold  of  the  whole  thickness  of  each  piece. 

Fig.  4  is  a  section  of  a  bridge  of  this  construction, 
and  shows  the  manner  in  which  the  braces  and 
string  pieces  come  together,  and  also  the  manner  of 
making  the  floor  of  the  bridge,  and  of  butting  beams 
and  braces  over  head,  which  are  to  be  connected 
with  the  middle  truss  for  the  purpose  of  bracing  the 
bridge  against  lateral  rack  or  motion.  Very  flat- 
pitched  roofs  will  be  preferable,  as-  they  will,  in  that 
case,  be  a  greater  support  to  the  upper  part  of  the 
bridge. 

a  a  a  a,  Fig.  1,  show  the  elevation  of  the  roof. 

Fig.  2  is  the  floor  or  plan  of  the  bridge,  showing 
the  mode  of  bracing  and  the  floor  joist. 

Fig.  4  is  a  view  of  the  bottom  or  top  edge  of  the 
string  piece,  and  shows  how  the  joints  are  broken  in 
using  the  plank,  and  also  how  the  trunnels  are  dis- 
turbed. 

This  mode  of  construction  will  have  the  same 
advantages  in  iron  as  in  wood,  and  some  in  cast 
iron  which  wood  has  not,  viz.,  that  of  reducing 
the  braces  in  size  between  the  joints,  and  of  cast- 
ing flaunches  to  them  where  they  intersect,  thereby 
making  it  unnecessary  to  have  more  than  one  bolt 
and  nut  to  each  joint  or  intersection. 

When  it  is  considered  that  bridges,  covered  from 
the  weather,  will  last  seven  or  eight  times  as  long  as 
those  not  covered,  and  that  the  cheapness  of  this 
mode  will  admit  of  its  being  generally  adopted,  with 
openings  or  spans  between  piers  composed  of  piles, 
and  at  a  distance  of  one  hundred  and  twenty  to  one 
hundred  and  sixty  feet  apart,  then  the  construction 
of  long  bridges  over  mud-bottomed  rivers,  like  those 
at  Washington,  Boston,  Norfolk,  Charleston,  &c.,  wiU 
be  perceived  to  be  of  great  importance,  especially  as 
the  common  mode  of  piling  is  so  exposed  to  freshets, 
uncommon  tides,  driftwood,  and  ice,  as  not  to  insure 
safety  or  economy  in  covering  them,  and,  conse- 
quently, continual  repairs,  and  often  rebuilding  them, 
become  necessary.  There  is  very  little,  if  any,  doubt 
that  one  half  of  the  expense,  computing  stock  and 
interest,  that  would  be  required  to  keep  up,  for  one 
hundred  years,  one  of  the  common  pile  bridges,  like 
those  at  Boston,  would  be  sufficient  to  maintain  one 
built  in  this  new  mode,  keep  it  covered,  and  have  all 


BRIDGES. 


131 


or  nearly  all,  the  piers  built  with  stone  at  the  end  of 
the  one  hundred  years.  If  this  be  the  case,  it  would 
be  great  economy  to  commence  rebuilding,  by  de- 
grees, in  this  manner.  The  saving  in  the  one  article 
of  floor  planks,  if  kept  dry,  would  be  very  great,  as, 
by  being  so  much  wet,  they  rot  and  wear  out  in  about 
hair  the  time. 

For  aqueduct  bridges  of  wood  or  iron,  no  other 
mode  can  be  as  cheap  or  answer  as  well.  This  mode 
has  equal  advantages  also  in  supporting  wide  roofs 
of  buildings,  centres  of  wide  arches  in  masonry, 
trussed  floorings,  partitions,  sides  of  wood  towers, 
steeples,  &c.,  6cc.,  of  public  buildings,  as  it  requires 
nothing  more  than  common  planks,  instead  of  long 
timber  —  being  much  cheaper,  easier  to  raise,  less 
subject  to  wet  or  dry  rot,  and  requiring  no  iron  work. 

Some  of  the  advantages  of  constructing  bridges 
according  to  this  mode  are  the  following:  — 

1.  There  is  no  pressure  against  abutments  or  piers, 
as  arched  bridges  have,  and,  consequently,  perpendic- 
ular supports  only  are  necessary :  this  saving  in  wide 
arches  is  very  great,  sometimes  equal  to  a  third  part 
of  the  whole  expense  of  the  bridge. 

2.  The  shrinking  of  timber  has  little  or  no  effect, 
as  the  strain  upon  each  plank  of  the  trusses,  both  of 
the  braces  and  string  pieces,  is  an  end-grain  strain  or 
lengthwise  of  the  wood. 

3.  Suitable  timber  can  be  easily  procured  and 
sawed  at  common  mills,  as  it  requires  no  large  or 
long  timber ;  defects  in  timber  may  be  discovered, 
and  wet  and  dry  rot  prevented,  much  more  easily  than 
could  be  m  large  timber. 

4.  There  is  no  iron  work  required,  —  which,  at  best, 
is  not  safe,  —  especially  in  frosty  weather. 

5.  It  has  less  motion  than  is  common  in  bridges, 
and  which  is  so  injurious  and  frequently  fatal  to 
bridges ;  and,  being  in  a  horizontal  line,  is  much  less 
operated  upon  by  winds. 

6.  A  level  road  way  is  among  the  most  important 
advantages  of  this  mode  of  construction. 

7.  The  side  trusses  serve  as  a  frame  to  cover  upon, 
and  thereby  save  any  extra  weight  of  timber,  except 
the  covering  itself;  and  the  importance  and  economy 
of  covering  bridges  from  the  weather  is  too  well  un- 
derstood to  need  recommendation  after  the  experi- 
ence which  this  country  has  already  had. 

8.  Draws  for  shipping  to  pass  through  may  with 
perfect  safety  be  introduced  in  any  part  of  the  bridge 


without  weakening,  as  in  arched  bridges,  where  llu' 
strength  and  safety  of  the  arches  depend  so  much  on 
their  pressure  against  each  other  and  abutments,  tiiat 
a  draw,  by  destroying  the  connection,  weakens  the 
whole  superstructure. 

9.  The  great  number  of  nearly  equal  parts  ov  joints 
into  which  the  strain,  occasioned  by  a  great  weight 
upon  the  bridge,  is  divided,  is  a  very  important  ad- 
vantage over  any  other  mode,  as,  by  dividing!;  the 
strain  or  stress  into  so  many  parts,  that  which  falls 
upon  any  one  part  or  joint  is  easily  sustained  by  it 
without  either  the  mode  of  securing  the  joints,  or  the 
strength  of  the  materials  being  sufficient. 

10.  The  expense  of  the  superstructure  of  a  bridge 
would  not  be  more  than  from  one  half  to  two  thirds 
of  other  modes  of  constructing  one  over  the  same 
span  or  opening.  This  is  a  very  important  considera- 
tion, especially  in  the  Southern  and  Western  States, 
where  there  are  many  wide  rivers,  and  a  very  scat- 
tered population  to  defray  the  expenses  of  bridges. 

11.  This  mode  of  securing  the  braces  by  so  many 
trunnels  gives  them  much  more  strength  when  they 
are  in  tension  strain  than  could  be  had  in  the  com- 
mon mode  of  securing  them  by  means  of  tenons  and 
mortises  ;  for  tenons  being  short,  and  not  very  thick, 
compared  with  this  mode,  nor  having  so  much  hold 
of  the  pins  or  trunnels  as  in  this  case,  will,  of  course, 
have  much  less  power  to  sustain  a  tension  or  pulling 
strain ;  and  it  is  obvious  that  this  strain  is  in  many 
cases  equal  to,  and  in  others  greater  than,  the  thrust 
or  pushing  strain.  It  is  also  very  obvious  that  this 
pushing  or  thrust  strain  in  the  mode  of  tenons  and 
mortises  receives  very  little  additional  strength  from 
the  shoulders  of  the  tenons,  as  the  shrinkage  of  the 
timber  into  which  the  tenon  goes  is  generally  so  much 
as  to  let  the  work  settle  so  far  as  to  give  a  motion 
or  vibration,  which,  in  time,  renders  them  weak  and 
insufficient. 

12.  Should  any  kind  of  arched  bridge,  for  any  rea- 
son, be  preferred,  however,  it  may  be  arched  either  at 
top  or  bottom,  or  both ;  still  this  same  mode  of  com- 
bining the  materials  will  have  all  the  advantages,  as 
to  cheapness  and  strength,  over  the  common  ones  of 
framing,  as  in  the  case  of  the  horizontal  or  straight 
ones  before  described.  Li  cases  where  abutments 
are  already  built,  it  may  sometimes  be  preferred. 

Sidewalks  may  with  equal  ease  be  constructed, 
either  on  the  outside  or  inside  of  the  main  body  of 


132 


BRIDGES. 


the  bridge,  which  particular,  us  also  the  great  strength 
of  the  mode,  &c.,  may  be  better  seen  by  examination 
of  the  models,  which  are,  or  soon  will  be,  placed  in 
most  of  the  principal  cities  of  the  United  States;  and 
no  merit  is  either  desired  or  claimed  in  this  new  mode 
of  construction  by  the  patentee  which  the  mode 
itself  docs  not  command,  even  on  the  most  strict 
philosophical  investigation,  as  to  its  mathematical 
principles,  the  easy,  practicable,  and  advantageous 
application  of  materials,  the  advantages  it  possesses 
in  mechanical  execution,  and  its  simplicity,  strength, 
economy,  and  durability,  as  a  general  and  uniform 
mode  of  bridge  building. 

Science  and  practice  will,  in  a  short  time,  decide  on 
this  question,  so  important  to  this  extensive  country. 

I  shall  conclude  this  article  by  a  few  ideas  taken 
from  the  celebrated  Robert  Fulton's  Treatise  on  Ca- 
nal Navigation,  page  117  and  subsequent  pages. 

In  England,  the  attention  of  engineers  has,  of  late 
years,  been  much  engaged  on  bridges  of  iron.  These 
bridges,  as  experience  produces  courage,  are  progres- 
sively enlarging  their  dimensions ;  nor  should  I  be 
surprised  if  genius  should,  in  time,  produce  the  me- 
chanic rainbow  of  one  thousand  feet  over  wide  and 
rapid  rivers.  Li  crossing  the  rivers  in  such  countries 
as  Russia  and  America,  an  extensive  arch  seems  to 
be  a  consideration  of  the  first  importance,  as  the  riv- 
ers, or  even  rivulets,  in  time  of  rain,  suddenly  swell 
to  a  great  height ;  and  in  the  spring,  on  breaking  up 
of  ice,  the  immense  quantity  which  is  borne  down 
with  a  rapid  stream  would,  if  interrupted  by  small 
arches  and  piers,  collect  to  such  a  weight  as  ulti- 
mately to  bear  away  the  whole.  It  is,  therefore,  ne- 
cessary that,  in  such  situations,  an  arch  should  be 
extended  as  far  as  possible,  and  so  high  as  to  suffer 
every  thing  to  pass  through,  or  the  inhabitants  must, 
without  some  other  expedient,  submit  their  passage 
to  the  casualties  of  the  weather. 

The  important  objection  to  bridges  of  wood  is  their 
rapid  decay ;  and  this  objection  is  certainly  well 
founded  when  particular  situations  are  alluded  to 
where  timber  is  scarce,  and,  consequently,  expensive. 
But  in  such  countries  as  America,  where  wood  is 
abimdant,  I  conceive  it  will  be  a  fair  criterion  to 
judge  of  their  application  by  calculating  on  the  ex- 
pense of  a  bridge  of  stone  and  one  of  wood,  and 
then  compare  the  interest  of  the  principal  saved  in 


adopting  the  wood  bridge  with  the  expense  of  its 
annual  repairs. 

I  have  before  exhibited  the  necessity  of  construct- 
ing bridges  in  America  of  an  extensive  span  or  arch, 
in  order  to  suffer  the  ice  and  collected  waters  to  pass 
without  interruption  ;  and  for  this  purpose,  it  must 
be  observed  that  a  wood  arch  may  be  formed  of  a 
much  greater  length  or  span  than  it  is  possible  to 
erect  one  of  stone  :  hence  wooden  bridges  are  appli- 
cable to  many  situations  where  accumulated  waters, 
bearing  down  trees  and  fields  of  ice,  would  tear  a 
bridge  of  stone  from  its  foundation. 

It  therefore  becomes  of  importance  to  render  bridges 
of  wood  as  permanent  as  the  natm'e  of  the  material 
will  admit. 

Hitherto,  in  bridges  not  covered  from  the  weather, 
the  immense  quantity  of  mortises  and  tenons,  which, 
however  well  done,  will  admit  air  and  wet,  and,  con- 
sequently, tend  to  expedite  the  decay  of  the  weak 
parts,  has  been  a  material  error  in  constructing  bridges 
of  wood. 

But  to  render  wood  bridges  of  much  more  impor- 
tance than  they  have  hitherto  been  considered  —  first, 
from  their  extensive  span ;  secondly,  from  their  dura- 
bility—  two  things  must  be  considered:  first,  that  the 
woodworks  should  stand  clear  of  the  stream  in  every 
part,  by  which  it  never  would  have  any  other  weight 
to  sustain  than  that  of  the  usual  carriages  ;  secondly, 
that  it  will  be  so  combined  as  to  exclude,  as  much  as 
possible,  the  air  and  rain. 

When  the  true  principle  of  building  bridges  of 
wood  is  discovered,  their  progressive  extension  is  as 
reasonable  as  the  increased  dimensions  of  shipping, 
which,  in  early  ages,  was  deemed  a  great  work,  if 
they  amomited  to  one  hundred  tons'  burden ;  but 
time  and  experience  have  extended  the  art  of  ship 
building  to  two  thousand  tons,  and  in  the  combina- 
tion and  arrangement  of  the  various  and  complicated 
parts  there  certainly  is  more  genius  and  labor  re- 
quired than  in  erecting  a  bridge  of  five  hundred  or 
one  thousand  feet  span.  But  the  great  demand  for 
shipping  has  rendered  their  formation  familiar,  and 
their  increased  bulk  has  gradually  grown  upon  our 
senses.  But  had  a  man,  in  the  infancy  of  naval 
architecture,  hinted  at  a  vessel  of  two  thousand  tons, 
I  am  inclined  to  think  his  contemporary  artists  would 
have  branded  him  as  a  madman. 


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BRIDGES. 


133 


WATERLOO     BRIDGE. 

Plate  95. 

This  bridge,  thrown  over  the  River  Thames,  at 
London,  was  projected  by  Mr.  George  Dodd,  about 
the  year  1805.  Considerable  time,  however,  elapsed 
before  the  iiltimate  arrangements  necessary  to  carry 
it  into  execution  were  made.  The  first  act  was  ob- 
tained in  the  month  of  June,  1809,  and  incorporated 
the  proprietors  under  the  name  of  the  "  Strand  Bridge 
Company,"  empowering  them  to  raise  the  sum  of 
£500,000  in  transferrable  shares  of  £100  each ;  and 
the  further  sum  of  £300,000,  by  the  issuing  new 
shares,  or  by  mortgage,  in  case  it  should  be  found 
necessary.  In  July,  1813,  a  second  act  was  passed, 
enabling  them  to  raise  an  additional  sum  of  £200,000 ; 
and  in  July,  1816,  a  third  act  was  obtained,  granting 
the  company  further  powers,  and  changing  the  name 
from  Strand  Bridge  to  Waterloo  Bridge,  which  name 
it  now  bears. 

IVIr.  Rennie,  having  been  appointed  engineer  to  the 
company  on  the  23d  day  of  June,  1810,  furnished  two 
designs,  one  of  seven  and  the  other  of  nine  arches, 
the  latter  of  which  was  finally  approved  by  the  com- 
mittee and  ordered  to  be  put  in  execution. 

This  noble  bridge  is  situated  about  half  way  be- 
tween the  Bridges  of  Blackfriars  and  Westminster. 
The  river  at  this  place  is  about  1326  feet  wide  at 
high  water ;  and  ordinary  spring  tides  rise  about  13 
feet,  and  ordinary  neap  tides  about  9  feet  6  inches. 
The  greatest  depth  at  low  water  is  about  9  feet.  The 
bed  of  the  river  is  composed  principally  of  a  stratum 
of  sand  and  gravel  resting  upon  clay. 

The  bridge  is  level,  and  consists  of  nine  semi-ellip- 
tical arches,  each  having  a  span  of  120  feet,  and  a 
rise  of  35  feet ;  thus  leaving  for  the  navigation  30 
feet  of  clear  height  above  the  high  water  of  spring 
tides,  and  forming  an  ample  water  way  of  1080  feet. 
The  abutments  are  40  feet  thick  at  the  bases,  and 
diminish  to  30  feet  at  the  springing  of  the  arches. 
Their  lengths,  including  the  stairs,  are  140  feet.  The 
piers  are  30  feet  broad  at  the  base,  and  diminish  to 
tw^o  thirds  at  the  springing  of  the  arches.  Their 
lengths  at  the  bases  are  87  feet.  The  points  or  sa- 
lient angles  of  the  piers  are  in  the  form  of  a  Gothic 
arch,  and  are  terminated  above  by  two  three-quarter 
columns,  supporting  an  entablature  which  forms  a 
recess.  The  whole  is  surmounted  with  a  balustrade 
and  a  frieze  and  cornice  of  the  Grecian  Doric.     The 


columns  are  Doric  also,  and  were  selected  on  account 
of  the  extraordinary  strength  of  their  proportions,  as 
being  best  suited  to  a  structure  of  this  magnitude : 
they  are  23  feet  9  inches  high,  or,  rather,  more  than 
four  diameters. 

The  clear  width  between  the  parapets  is  42  feet  4 
inches,  allowing  28  feet  4  inches  for  the  carriage-way, 
and  7  feet  for  each  of  the  footpaths. 

Four  plying  places,  or  stairs,  for  watermen,  are 
formed  by  circular  wings,  projecting  at  right  angles 
to  the  bridge,  with  archways  leading  to  the  road  way. 
These  wings  are  ornamented  with  columns,  entabla- 
tures, &c.,  as  before  described. 

The  bridge  being  level,  and  of  so  great  a  length,  it 
became  necessary  to  provide  means  for  carrying  off 
the  rain  water.  This  is  efiectcd  by  having  circular 
openings  in  the  centre  of  each  pier,  which  enter  the 
river  immediately  below  low-water  mark  ;  these  open- 
ings are  connected  with  iron  branch  pipes  up  to  the 
level  of  the  road-way,  where  gratings  are  placed  to 
receive  the  water. 

The  roads,  or  approaches,  to  each  end  of  the  pier 
are  70  feet  wide  throughout,  except  just  at  the  en- 
trance into  the  Strand,  and  are  carried  over  a  series 
of  semicircular  brick  arches  of  16  feet  span  each. 
The  Surry,  or  southern  approach,  is  formed  by  39  of 
these,  besides  an  elliptical  arch  of  26  feet  span  over 
the  narrow  wall  road,  and  a  small  embankment 
about  165  yards  long,  having  an  easy  and  gradual 
ascent  of  not  more  than  1  foot  in  34  feet. 

Feet. 
The  length  of  the  brick  arches  in  the  Surry 

approach  is 766 

Ditto  of  those  in  the  Strand  approach,    .       .     310 
Total  length  of  the  bridge  from  the  ends  of 

the  abutments, 1380 

Total  length  of  the  bridge  and  brick  arches,    2456 

Fig.  1  exhibits  a  longitudinal  section  of  one  of  the 
arches,  the  adjacent  piers,  and  part  of  the  next  adja- 
cent arches,  with  the  elevation  of  one  of  the  trusses 
forming  the  centre.  The  curve  of  equilibrium  passes 
through  the  middle  of  the  length  of  the  arch  stones, 
or  very  nearly  so.  The  hollows  over  the  piers  are 
raised  to  the  level  of  the  summits  of  the  arches  by 
parallel  brick  walls,  and  connected  with  blocks  of 
stone  from  wall  to  wall,  for  supporting  the  road-way. 

The  centring  was  composed  of  eight  trusses.  It 
is  1250  feet  long,  has  nine  elliptical  arches  of  120  feet 


134 


RURAL     VILLA.— CHURCH    EDIFICE. 


span  over  the  river,  with  piers  20  feet  thick,  built  en- 
tirely of  granite,  and  forty  brick  arches  for  a  cause- 
way on  the  Surry  side.  This  plate  is  given  with  a 
view  of  showing  the  construction  of  masonry,  as  gen- 
erally applied  to  bridge  building.  The  geometrical 
principle  of  constructing  arches,  and  drawing  the 
joint  Lines  so  as  to  be  perpendicular  to  the  curve,  is 
sufficiently  explained  in  plate  101. 

Fig.  2.  The  horizontal  section  showing  the  brick 
walls,  as  a,  a,  &c.,  which  arc  covered  with  stone ; 
also,  the  foundation  of  the  piers  at  b,  b,  &c. 


RURAL     VILLA    AT     MILFORD,    MASS. 

Plate  96. 

On  this  plate  we  have  given  a  front  elevation,  with 
a  transverse  section,  together  with  the  entrance  and 
chamber-story  plans  of  a  villa  that  we  have  erected 
during  the  past  year,  in  the  town  of  MUford,  Mass., 
for  A.  C.  Mayhew,  Esq.  It  was  our  intention  at 
first  to  place  at  the  last  part  of  this  work  a  series  of 
six  designs  for  buildings  of  this  character,  with  their 
plans  and  detailg ;  but  upon  further  consideration  we 
have  concluded  to  omit  them,  and,  at  some  future 
time,  publish  them  in  a  form  more  in  keeping  with 
a  work  of  a  rural  character;  this  plate,  however, 
being  made,  we  have  inserted  it  as  plate  96. 
The  size  of  the  building  will  be  readily  seen  by 
the  figures  on  the  drawing.  The  outside  walls 
are  of  hard-burnt  bricks,  and  are  twelve  inches 
in  thickness,  which  are  vaulted,  or  having  an  air 
space  of  four  inches  between  the  exterior  and  inte- 
rior courses.  The  angles  of  the  buUding  are  laid 
solid,  as  are  also  the  sides  of  the  openings  in  the 
walls,  such  as  the  sides  of  the  doors,  windows,  &e. 
The  vaulted  portions  are  connected  together  by 
means  of  ties  of  brick  in  every  two  feet  in  length. 
The  exterior  walls  are  covered  with  stucco  cement, 
and  colored  in  imitation  of  drab  stone.  The  exte- 
rior wood  work  is  painted,  and  sanded  with  beach 
sand.  —  Editors. 


CHURCH  EDIFICE  AT  MILFORD,  MASS. 

Plate  97. 

On  this  plate  will  be  found  the  t%vo  plans,  and  the 
front  elevation  of  a  small  church  which  was  erected 


under  our  superintendence  in  1850,  for  the  Pearl 
Street  Universalist  Society  of  JMilford,  Mass.  We 
do  not  present  it  as  containing  any  thing  of  pecu- 
liar merit  or  of  costly  design ;  but  the  arrangement 
of  the  plans  and  tlie  general  features  of  the  build- 
ing having  received  the  approval  and  approbation 
of  building  committees  and  others  interested  in 
such  matters,  we  have,  at  their  urgent  solicitations, 
and  at  the  suggestions  of  many  others,  inserted  this 
plate  for  the  benefit  of  those  seeking  the  information 
the  plate  and  its  description  may  contain.  The  fol- 
lowing description  of  this  edifice  appeared  in  the 
Trumpet  and  Universalist  Magazine  at  the  time  the 
budding  was  dedicated ;  and,  with  a  few  slight  alter- 
ations, we  transcribe  it  entire,  as  the  description  of 
plate  97.* 

ARCHITECTURAL  DESCRIPTION  OF  THE  NEW  MEET- 
ING-HOUSE IN  MILrORD,  IIASS. 

This  building  is  built  of  wood,  erected  upon  a  brick  stylobate  or 
basement,  and  is  of  the  following  dimensions,  viz.,  length,  72  feet 
8  inches;  width,  51  feet,  outside;  with  a  projecting  vestibule  on 
the  front  end,  13  feet  wide  by  26  feet  long,  and  the  posts  are  25  feet 
in  height.  Upon  the  roof  of  the  vestibule  stands  a  pedestal,  19  feet 
square  and  13  feet  high,  finished  with  suitable  projections  ;  upon 
this  is  a  clock  tablet,  15  feet  square  and  12  feet  high,  covered  with 
a  roof  showing  an  entablature  and  pediment  on  each  side  ;  the  tab- 
let is  finished  with  heavy  mouldings,  and  a  recess  8  inches  deep  is 
made  on  each  side,  to  receive  a  dial  7  feet  in  diameter.  Rising  from 
this  is  an  octagonal  bell  tower,  12  feet  in  diameter  and  IG  feet  high, 
including  its  base  and  entablature  ;  on  each  of  its  sides  are  arched 
openings,  3  feet  3  inches  in  width,  and  in  each  of  which  is  a  balus- 
trade, composed  of  heavy-turned  balusters.  Upon  this  tower  is  an 
octagonal  pedestal,  6  feet  high  and  11  feet  in  diameter,  with  deep 
panels  on  each  side,  which  is  surmounted  by  a  spire  45  feet  high, 
crowned  with  a  carved  finial,  making  the  entire  height  from  the  line 
of  the  grading  136  feet.  The  style  of  architecture  Is  the  Roman- 
esque, which  is  a  combination  of  the  Roman  and  the  late  Norman, 
the  latter  being  the  prevailing  style  of  the  11th  century.  The  cor- 
ners of  the  building,  together  with  the  vestibule,  are  finished  with 
heavy  pUasters  2  feet  9  inches  wide,  in  each  of  which  is  a  deep 
circular-headed  panel ;  upon  these  rests  a  dentil  corniced  entablature, 
5  feet  deep.  The  cornice  of  the  entablature  is  continued  up  the 
rakes  of  the  main  building  and  vestibule,  which  finish  gives  the 
whole  an  imposing  and  massive  appearance. 

The  building  is  Ughted  on  either  side  by  three  circular-headed  win- 
dows, which  arc  composed  of  two  circular-headed  parts,  and  separated 
by  a  large  mullion  ;  and  the  front  of  the  main  building,  on  either  side 
of  the  vestibule,  by  one  of  the  same  style,  and  of  two  thirds  the  width 

*  To  OUn  BELOVED  FRIENU,  THE  ReV.  HeNRT  A.  EaTON,  PAS- 
TOR OP  TUE  SOCIETY,  AND  UNDER  WHOSE  MINISTRATIONS  TUB 
BUILDING  WAS  ERECTED,  THIS  PLATE  IS  RESPECTFULLY  DEDI- 
CATED, A3  A  SMALL  TRIBUTE  OF  RESPECT  AND  ESTEEM,  BY  THE 
ARCHITECTS. 

THOMAS  W.  SILLOWAY, 
GEORGE  M.  HARDING. 


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CHURCH    EDIFICE. 


of  those  on  the  sides,  making  them  adapted  to  their  location.  The 
choir-room,  which  is  on  the  second  floor  of  the  vestibule,  is  lighted 
by  a  largo  window,  composed  of  one  in  its  centre,  similar  to  those 
before  described ;  to  which  is  added  on  either, side  another  of  one 
half  its  width,  and  a  proportionate  height,  and  separated  from  it  by 
pilasters,  the  capitals  of  which  are  so  disposed  that  the  centre  ■win- 
dow is  stilted  1  foot  6  inches ;  the  i\idth  of  the  entire  window  is  1 1 
feet.  Beneath  this  window,  on  the  front  of  the  vestibule,  is  the 
main  entrance  to  the  building,  which  is  by  three  circular-headed 
doors,  the  centre  one  of  which  is  5  feet  wide  suid  13A  feet  high  ;  the 
arch  of  this  door  is  stilted  3  feet.  Those  of  cither  side  are  34  feet 
wide  and  10  feet  3  inches  high;  making  an  actual  space  in  width 
of  12  feet,  which  is  1  foot  6  inches  more  than  the  whole  width  of  the 
church  aisles.  The  doors  are  entered  by  five  steps,  which  are  buUt 
of  southern  pine,  and  extend  the  entire  length  of  the  vestibule,  in- 
cluding a  buttress  3  feet  wide  at  either  end.  This  brings  us  to  the 
interior  of  the  building. 

As  has  been  before  stated,  the  entrance  was  but  five  steps  from 
the  grading  on  the  front  end,  so  that  the  entrance  floor  is  five  feet 
lower  than  the  pew  floor  ;  a  space  of  four  feet  is  left  at  the  entrance 
on  the  inside,  the  entire  length  of  the  vestibule,  24  feet.  And  at 
that  distance  from  the  doors,  a  flight  of  eight  stairs,  13  feet  long, 
lead  up  to  the  entry  of  the  church  ;  which  entry  is  74  feet  wide, 
and  runs  the  entire  width  of  the  church  on  the  inside.  These  stairs 
are  very  easy  of  ascent,  and,  being  13  feet  long,  amoimt  to  24  feet 
more  than  the  width  of  all  the  aisles,  so  that  these,  together  with 
the  outside  doors,  insure  against  any  jam  being  produced  in  the 
entry  of  the  building,  which  is  one  of  the  evUs  with  which  the 
architect  has  often  to  contend. 

On  either  side  of  the  main  stairs  to  the  church  arc  those  leading 
to  the  vestry ;  these  are  each  44  feet  wide,  making  a  passage-way 
of  9  feet ;  they  are  built  of  southern  pine,  as  are  also  the  floors  of 
all  the  entries,  and  are  oiled  over,  leaving  the  natural  color  of  the 
wood.  A  large  mahogany  rail  and  southern  pine  balusters  com- 
mence at  the  foot  of  those  to  the  vestry,  and  are  continued  up 
around  the  well-room  over  those  to  the  church,  and  returns  at 
the  top  railing  in  the  space  on  the  upper  entry,  which  is  not 
occupied   by  those  leading  to  the  entrance  floor. 

An  arch  is  sprung  over  each  of  the  three  openings  at  the  top  of  the 
church  stairs  ;  these  openings  are  made  by  a  square  pillar  coming 
down  at  the  head  of  the  stairs  on  either  side,  so  that,  beneath  these 
three  arches,  the  whole  space  is  open  on  the  church  entry  floor  the 
entire  ^vidth  of  the  vestibule,  which  gives  to  the  whole  a  spacious 
and  airy  appearance.  From  this  floor,  stairs  on  either  end  lead  to 
the  singing  gallery.  Beneath  this  entry,  on  the  vestry  floor,  is  one 
of  the  same  width,  and  from  it  is  a  door  4  feet  wide,  leading  to  the 
outside  of  the  building  ;  one  leading  to  a  room  12  feet  square,  for 
wood  and  coal,  beneath  the  church  stairs  ;  also  two  others  leading 
to  the  vestry,  the  dimensions  of  which  are  42  by  49  feet,  and  1 1  feet 


high  in  the  clear  ;  connected  with  which  arc  two  ante-rooms,  each 
20  feet  6  inches  by  22  feet.  Attached  to  each  of  these  rooms  is  a 
closet,  4  feet  wide  and  U  feet  long.  The  ante-rooms  are  separated 
from  the  vestry  by  largo  doors,  which  move  on  castors,  so  that  the 
whole  may  be  thrown  into  one  large  room. 

The  floor  of  the  church  contains  82  pews,  2  feet  10  inches  wide, 
and  9  feet  7  inches  in  length,  which  provides  19  inches  to  a  person, 
allowing  G  persons  to  a  pew,  making  the  house  capable  of  seating  in 
all,  including  the  gallery,  650  persons.  Tlie  side  aisles  are  3  feet 
wide ;  the  one   in  the  centre,  44  feet. 

The  pulpit  is  of  an  original  design,  and  is  in  strict  accord- 
ance with  the  architectural  character  of  the  edifice.  It  is  an  im- 
itation of  rosewood,  and  the  seven  circular-headed  panels  on  the 
front  are  lined  with  garnet  plush.  The  sofa  connected  with  the 
pulpit  is  of  rosewood,  and  was  designed  for  the  place  it  occupies ; 
the  trimmings  of  the  sofa,  pulpit,  and  chairs  are  also  of  garnet 
plush. 

There  is  a  choir  gallery  at  the  end  of  the  church,  over  the 
entrance,  connected  with  which  is  a  room  for  the  choir's  rehear- 
sals, 24  by  12  feet,  and  12  feet  high.  There  ia  a  dado  in  each 
of  the  side  aisles  of  the  main  floor,  to  the  height  of  the  window 
sUls,  which  is  returned  at  the  sides  of  each  window,  making  a 
pedestal  of  sufficient  width  to  include  the  window  and  the  fresco 
pilasters  at  its  sides.  This  dado  has  a  capping  and  base,  which, 
together  with  the  doors  of  the  church,  are  grained  black  walnut. 

The  windows  of  the  whole  building,  above  the  basement,  are 
furnished  with  blinds  on  the  inside,  and  are  painted  Paris  green. 
The  walls  of  the  principal  room  arc  24  feet  high,  and  these,  with  the 
whole  interior  of  the  church,  are  finely  painted  in  distemper  fresco, 
in  the  following  manner  :  The  side  walls  have  a  fine  fluted  Corin- 
thian pilaster  on  each  side  of  all  the  windows,  which  support  an 
entablature  3  feet  deep,  extending  entirely  around  the  church  walls ; 
between  each  of  these  is  a  sunken  panel,  and  inside  of  these  is  one 
which  is  raised ;  over  the  windows  is  a  rich  moulding  ornamented 
with  a  console,  and  ending  at  the  pilasters  with  an  acanthus  lea£ 
On  the  back  end,  on  either  side  of  the  recess,  back  of  the  pul- 
pit, is  painted  a  niche  standing  on  a  pedestal,  and  finished  like  the 
windows.  In  the  recess  back  of  the  pulpit  is  represented  an  arched 
panelled  recess  or  passage,  leading  to  a  rotunda,  in  the  centre  of 
which  stands  a  large  cross ;  the  celling  is  very  finely  decorated  by 
large  panels,  and  at  the  angles  are  ornaments  of  Roman  foliage, 
extending  some  11  feet  either  way.  In  the  centre  of  the  ceiling  is 
a  cast-iron  register,  3  feet  in  diameter,  to  admit  the  foul  air  to  one 
of  Emerson's  ventilators,  (which  efi'ectually  ventilates  the  room;) 
around  this  is  a  beautiful  design  of  foliage,  and  on  two  of  its  sidei 
is  seen  a  harp,  supported  by  the  leaves  and  scroUs.  The  tint  of  the 
ground  is  a  gray  lilac.  The  building  was  raised  in  November  last, 
and  has  been  entirely  completed  since  that  time.  It  has  cost, 
including   the  land   and  furnishing,   not  far  from  $10,500. 

T.  W.  S. 


136 


GOTHIC    ARCHITECTURE. 


GOTHIC   ARCHITECTURE 


Gotliic,  or  what  may  be  termed,  with  more  pro- 
priety, English  architecture,  is  that  style  which  im- 
mediately succeeded  the  Norman,  and  the  most 
prominent  feature  of  which  is  the  pointed  arch, 
slender  columns,  and  a  predominancy  of  vertical 
lines.  Wc  should  have  been  pleased  to  have  given 
a  full  description  of  this  kind  of  architecture  ;  but 
our  limits  not  permitting,  we  shall  content  ourselves 
with  simply  giving  a  synopsis  of  some  of  its  char- 
acteristics; and  to  those  of  our  patrons  who  may 
wish  for  a  more  extensive  knowledge  of  this  branch 
of  the  science,  we  would  refer  them  to  a  work 
known  as  the  Glossary  of  Architecture,  the  fifth 
edition  of  which  was  published  in  London  the  past 
year.  This  work  contains  a  very  elaborate  description 
of  all  that  pertains  to  this  branch  of  the  science,  and 
is  a  production  of  inestimable  value.  We  have 
stated  that  this  species  of  architecture  immediately 
succeeded  the  Norman  —  indeed,  it  is  a  work  of 
some  nicety  to  draw  the  dividing  line  between  them ; 
but,  before  proceeding  further,  we  will  remark  that 
the  Rev.  Mr.  Millers,  of  England,  has  divided  the 
architecture  on  which  we  treat  into  three  distinct 
classes,  and  his  classification  has  met  the  approval 
of  Rickman  and  Pugin,  who  are  among  the  principal 
architectural  \\Titers  of  England.  The  first  style  he 
terms  the  Early  English,  the  second  the  Decorated, 
and  the  third  the  Perpendicular.  We  shall  follow 
him  in  this  respect,  and  shall  describe  each  style  re- 
spectively hereafter. 

The  Early  English,  then,  is  the  style  which  is 
nearest  to  the  Norman,  and  it  may  be  said  to  have 
grown  out  of  it ;  and  here  we  beg  leave  to  differ 
from  the  opinion  that  has  at  times  found  warm 
advocates,  which  is,  that  the  form  of  the  arch  which 
characterizes  this  species  of  architecture  was  sug- 
gested by  the  intersection  of  branches  of  trees.  This 
idea  is,  without  doubt,  the  production  of  a  fertile 
imagination,  and,  like  the  famous  story  of  Callima- 
chus  and  the  vase  at  Corinth,  it  may  be  regarded  as 
a  play  of  the  fancy  and  a  freak  of  ideality.  One  of 
the  principal  features  of  the  Norman  architecture  is 


the  very  frequent  use  of  the  Roman  arch ;  and,  by 
describing  a  second  semicircle  with  a  point  in  the 
circumference  of  one  already  drawn  as  a  centre,  we 
produce  what  is  familiarly  known  as  the  Gothic  arch, 
and  a  series  of  these  we  term  intersected  arches. 
This  also  is  of  firequent  occurrence  in  the  later 
Norman  architecture ;  and  we  deem  it  no  departure 
from  the  principles  of  logic  to  deduce  from  this  fact 
that  the  arch  used  in  the  English  architecture  was 
no  invention,  but  simply  a  transfer  to  it  from  the 
Norman,  and  that,  even  with  those  with  whom  it 
originated,  it  was  the  result  of  accident  rather  than 
design.  We  thus  give  our  reasons  for  the  intrusion 
we  make  upon  the  favorite  speculations  of  those 
who  may  differ  from  us,  for  we  do  so  with  all  re- 
spect to  their  love  of  the  ideal,  and  we  would  be  the 
last  to  deprive  them  of  the  pleasure  they  may  de- 
rive from  the  idea  that  those  with  whom  one  of  the 
most  beautiful  of  the  productions  of  architecture  had 
its  origin  were  men  endowed  with  great  inventive 
talent,  and  that,  too,  which  often  manifested  itself  to 
an  astonishing  degree.  But  to  proceed:  we  will 
again  remark,  that  the  first  style  is  the  Early  English, 
and  is,  as  its  name  suggests,  the  earliest  of  the  three. 
The  intersecting  arches  to  which  we  have  before 
referred  characterized  the  Norman,  as  it  was  about 
to  merge  into  it,  and,  in  some  instances,  we  find 
examples  of  the  poiiited  arch  in  the  Norman,  entirely 
by  itself;  thus  the  one  has  produced  the  other. 

The  time  when  this  style  may  be  said  to  have  had 
its  rise  was  about  the  year  1200,  and  continued  from 
this  period  to  1300,  which  extended  through  the  reigns 
of  John,  Henry  III.,  and  Edward  I.  It  is  stated  that, 
during  the  reign  of  Henry  III.  alone,  no  less  a  num- 
ber than  one  hundred  and  fifty-seven  abbeys,  priories, 
and  other  religious  houses  were  founded  in  England ; 
and  the  erection  of  these  was  considered  as  among 
the  most  effectual  means  of  obtaining  the  forgiveness 
of  sins,  and,  consequently,  the  favor  of  Heaven. 
The  principal  characteristic  of  this  style  is,  in  the 
language  of  Gwilt,  as  follows :  The  arches  are 
sharply  lancet  pointed,  and  lofty,  in  proportion  to 


GOTHIC    ARCHITECTURE. 


137 


their  span.  In  the  upper  tiers,  two  or  more  are  com- 
preliended  under  one,  finished  in  trefoil  or  cinquefoil 
heads,  instead  of  points,  the  separating  columns 
being  slender.  Columns  on  whicii  the  arches  rest 
are  very  slender  in  proportion  to  their  iieight,  and 
usually  consist  of  a  central  shaft,  surrounded  by 
several  smaller  ones.  The  base  takes  the  form  of 
the  cluster  and  the  capital  is  frequently  decorated 
with  foliage,  very  elegantly  composed.  The  tcin- 
doics  are  long,  narrow,  and  lancet-shaped,  whence 
some  \\Titers  have  called  this  style  the  Lancet  Gothic. 
They  are  divided  by  one  plain  mullion,  or,  in  upper 
tiers,  by  two  at  most,  finished  at  the  top  with  some 
simple  ornament,  as  a  lozenge,  or  a  trefoil.  They 
have  commonly  small  marble  shafts  on  each  side, 
both  internally  and  externally ;  two,  three,  or  more, 
together,  at  the  eas't  or  west  end,  and  tier  above  tier. 
Roofs  arc  high  pitched,  and  the  ceilings  vaulted, 
exhibiting  the  first  examples  of  arches  with  cross 
springers  only,  which,  in  a  short  period,  diverged  into 
many  more,  rising  from  the  capitals  of  the  columns, 
and  almost  overspreading  the  whole  sm-face  of  the 
vaulting. 

The  longitudinal  horizontal  line  which  reigned 
along  the  apex  of  the  vault  was  decorated  with 
bosses  of  flowers,  figures,  and  other  fancies.  Walls 
much  reduced  in  thickness  from  those  of  the  pre- 
ceding period ;  they  arc,  however,  externally  strength- 
ened with  buttresses,  which,  as  it  were,  lean  against 
them  for  the  purpose  of  counteracting  the  thrust 
exerted  by  the  stone  vaults  which  form  the  ceil- 
ings, and  which  the  walls  and  piers,  by  their  own 
gravity,  could  not  resist.  The  buttresses  are,  more- 
over, aided  in  their  office  by  the  pinnacles,  adorned 
with  crockets  at  their  angles,  and  crowned  with 
fiuial  flowers,  by  which  they  are  surmounted.  The 
ornaments  now  become  numerous,  but  they  arc  sim- 
ple and  elegant.  The  mouldings  are  not  so  much 
varied  as  in  the  Norman  style,  and  are  generally, 
perhaps  universally,  formed  of  some  combination  of 
leaves  and  flowers,  used  not  only  in  the  cuxumference 
of  arches,  especially  of  windows,  but  the  columns  or 
pilasters  are  completely  laid  down  with  them  —  ti-e- 
foils,  quatrefoils,  cinqucfoils,  roses,  mullets,  bosses,  pa- 
terae, &c.,  in  the  spandrils,  or  above  the  keystones  of 
the  arches,  and  elsewhere.  The  ornamental  pinna- 
cles on  shrines,  tombs,  &c.,  are  extremely  high  and 
acute,  sometimes  with,  and  sometunes  without,  niches 
under  them.     In  east  and  west  fronts,  the  niches  are 

18 


filled  with  statues  of  the  size  of  life,  and  larger,  and 
are  crowned  with  trefoil,  &c.,  heads,  or  extremely 
acute  pediments,  formed  by  the  meeting  of  two 
straight  lines,  instead  of  arcs.  All  these  ornaments 
arc  more  sparingly  introduced  into  large,  entire  edi- 
fices than  in  smaller  buildings  or  added  parts.  The 
plans  are,  generally,  similar  to  those  of  the  preceding 
period;  but  that  important  feature,  the  tower,  now 
begins  to  rise  to  a  great  height,  and  lanterns  and 
lofty  spires  arc  frequent  accompaniments  to  the 
structure.  It  will  natm'ally  occur  to  the  reader,  that,  in 
tiie  transition  from  the  Norman  to  this  style,  the  archi- 
tects left  one  extreme  for  another,  though  it  has  been 
contended  that  the  latter  has  its  germ  in  the  former. 
However  that  may  be,  the  period  of  which  we  are 
now  speaking  was  undoubtedly  the  parent  of  the 
succeeding  styles,  and  that  by  no  very  forced  or  un- 
natural relationship. 

The  principal  examples  of  the  early  English  style, 
in  the  catheckal  churches  of  England,  are  to  be  seen 
at  Oxford,  in  the  chajiter-house  ;  Lincoln,  in  the  nave 
and  arches  beyond  the  transept ;  York,  in  the  north 
and  south  transept ;  at  Durham,  in  the  additional  tran- 
sept ;  Wells,  the  tower  and  the  whole  western  front ; 
Carlisle,  the  choir ;  Ely,  the  presbytery ;  Worcester, 
the  transept  and  choir ;  Salisbitri/,  the  whole  cathe- 
ch-al  —  the  only  unmixed  example  ;  at  Rochester,  the 
choir  and  transept.  "  It  is  well  worthy  of  observa- 
tion," says  Ml-.  Dallaway,  "  that  though  the  gi-ound 
plans  of  sacred  edifices  are,  generally  spealdng,  simi- 
lar and  systematic,  yet  in  no  single  instance  which 
occurs  to  my  memory  do  we  find  an  exact  and  un- 
varied copy  of  any  building  which  preceded  it,  in  any 
part  of  the  structure.  A  striking  analogy  of  resem- 
blance may  occur,  but  that  rarely." 

The  second  class  or  style  is  the  Decorated,  and  oc- 
cupied the  period  between  1300  and  1460.  "  Li  the 
early  part  of  the  period,"  continues  Gwilt,  "  the  change, 
or  rather  progress,  was  extremely  slow,  and  marked  by 
little  variation  ;  and  indeed,  until  1400,  the  style  can 
scarcely  be  said  to  have  been  perfected ;  but  after 
that  time,  it  rapidly  attained  all  the  improvement 
whereof  it  was  susceptible,  and  so  proceeded  till 
about  1460,  after  which  it  assumed  an  exuberance 
of  ornament,  beyond  which,  as  it  was  impossible  to 
advance,  it  was  in  a  predicament  from  which  no 
change  could  be  efiected  but  by  its  total  abandon- 
ment. This  style  exhibits  arches,  less  acute  and 
more  open,  the  forms  varying." 


138 


GOTHIC    ARCHITECTURE. 


Columns.  —  The  central  and  detached  shafts  are 
now  -worked  together  into  one,  from  experience  of  the 
weakness  of  those  of  the  previous  style,  exceedingly 
various  in  their  combinations. 

The  untulows  are  larger,  divided  by  mullions  into 
several  lights,  spreading  and  dividing  at  the  top  into 
leaves,  flowers,  fans,  wheels,  and  fanciful  forms  of 
endless  variety.  These  marks  are  constant,  but  in 
the  proportionate  breadth  there  is  much  variation ; 
for,  after  having  expanded  in  the  reigns  of  Edward  I. 
and  II.,  they  grew  narrower  again  in  proportion  to 
their  height  in  that  of  Edward  III.,  and  also  sharper. 
The  head  was  then  formed  of  lines  just  perceptibly 
curved,  sometimes  even  by  two  straight  lines,  some- 
times just  cur\-ed  a  little  above  the  haunches,  and  then 
rectilinear  to  the  apex.  The  eastern  and  western  win- 
dows were  very  lofty  and  ample,  and  splendidly  deco- 
rated with  painted  glass.  In  regard  to  the  roof  or 
ceiling,  the  vaulting  is  more  decorated.  The  princi- 
pal ribs  spread  from  their  imposts,  running  over  the 
vault  lilie  tracery,  or,  rather,  with  ti'ansoms  divided 
into  many  angular  compartments,  and  ornamented 
at  the  angles  with  heads,  orbs,  historical  or  legendary 
pictures,  &c.,  elaborately  colored  and  gilded.  The 
ornaments  are  more  various  and  labored,  but  not  so 
elegant  and  graceful  in  character,  as  in  the  preceding 
style.  Niches  and  tabernacles,  with  statues,  are 
used  in  great  abundance.  Tiers  of  small  ornamental 
arches  are  frequent.  The  pinnacles  arc  neither  so 
lofty  nor  tapering,  but  are  more  riclily  decorated  with 
leaves,  crockets,  &c.  Sculpture  is  introduced  in 
much  profusion,  and  is  frequently  painted  and  gilt; 
screens,  stalls,  doors,  panelled  ceilings,  and  other 
ornaments   in   carved   and   painted   wood. 

Some  of  tlie  principal  examples  of  the  ornamented 
English  style  in  cathedral  churches  are,  at  Exeter, 
the  nave  and  choir;  Lichfield,  uniformly;  at  Lincoln, 
the  additions  to  the  central  tower;  at  Worcester,  the 
nave ;  York,  nave,  choir,  and  western  front ;  at  Can- 
terbury, transept ;  at  Gloucester,  transept  and  cloisters 
began  ;  Norwich,  the  spire  and  tower ;  Salisbiiri/,  spire 
and  additions ;  Bristol,  the  nave  and  choir  ;  Chichester, 
the  spire  and  choir;  Eli/,  Our  Lady's  Chapel,  and 
the  central  louvre  ;  Hereford,  the  chapter-house  and 
cloisters,  now  destroyed.  In  the  later  part  of  the  pe- 
riod, the  choir  at  Gloucester,  the  nave  at  Canterbury, 
Bishop  Beckington's  additions  at  Wells,  and  from 
the  upper  transept  to  the  great  east  window  at 
Lincoln. 


FLORID     ENGLISH,    OR    PERPENDICU- 
LAR   STYLE. 

"  There  is,"  as  Dr.  Henry  obser^'es,  "  a  certain  per- 
fection in  art  to  which  hmnan  genius  may  aspire 
with  success,  but  beyond  which  it  is  the  apprehen- 
sion of  many  that  improvement  degenerates  into  false 
taste  and  fantastic  refinement."  "  The  rude  sim- 
plicity of  Saxon  architecture  was  [ultimately]  sup- 
planted by  the  magnificence  of  the  ornamental  Gothic; 
but  magnificence  itself  is  at  last  exhausted,  and  it 
terminated  dm-ing  the  present  period  in  a  style  cen- 
sm-able  as  too  ornamental,  departing  from  the  gran- 
dem-  peculiar  to  the  Gothic,  without  acquiring  pro- 
portional elegance;  yet  its  intricate  and  redundant 
decorations  arc  well  calculated  to  rivet  the  eye,  and 
amaze,  perhaps  bewilder,  the  mind."  The  period  of 
this  style  is  from  1460  to  the  dissolution  of  the  re- 
ligious houses  in  1537,  and  comprehends,  therefore, 
the  reigns  of  Edward  IV.  and  V.,  Richard  III., 
Henry  VII.  and   VIII. 

Its  principal  characteristics  are  arches,  univer- 
sally flat,  and  wide  in  proportion  to  their  height. 
The  windows  arc  much  more  open  than  in  the 
last  period,  flatter  at  the  top,  and  divided  in  the 
upper  part  by  transoms,  which  are  almost  con- 
stantly crowned  with  embattled  work  in  miniature. 
The  ceilings,  or  vaultings,  spread  out  into  such  a 
variety  of  parts  that  the  whole  surface  appears  cov- 
ered with  a  web  of  delicate  sculpture  or  embroidery 
thrown  over  it;  and  from  different  intersections  of 
this  ribbed  work,  clusters  of  pendent  ornaments  hang 
down,  as  Mr.  Miller  observes,  like  "  stalactites  in 
caverns."  The  flying  buttresses  are  equally  orna- 
mented, and  the  external  sufaces  of  the  walls  are  one 
mass  of  delicate  sculpture.  The  ornaments,  as  may 
be  deduced  from  the  above  particulars,  are  lavish  and 
profuse  in  the  highest  degi-ee.  Fretwork,  figures  of 
men  and  animals,  niches  and  tabernacles,  accompanied 
with  canopies,  pedestals,  and  traceries  of  the  most 
exquisite  workmanship,  carried  this  style  to  the  sum- 
mit of  splendor ;  and  all  these  combined  had,  perhaps, 
no  small  share  in  producing  the  extinction  it  was 
doomed  to  undergo. 

Roslin  and  Holyrood  Chapels,  the  first  whereof  was 
erected  by  Sir  William  St.  Clair,  for  richness  and 
variety  of  ornamental  carvings  camiot  be  exceeded. 
Its  plan  is  without  parallel  in  any  other  specimen  of 
the  fifteenth   century.     The  latter  was  finished  by 


GOTHIC    AKCHITECTURE. 


139 


James,  the  second  ol  that  name,  in  1440,  and  is  a 
beautiful  example,  with  flying  buttresses,  which  are 
more  ornamented  than  any  even  in  England.  Ex- 
amples of  tlie  Florid  Gothic  or  Perpendicidar  style 
are  to  be  seen  at  the  cathedi-al  churches  of  Glouces- 
ter, in  the  Chapel  of  Our  Lady ;  at  Oxford,  in  the 
roof  of  the  choir ;  at  Ely,  in  Alcock's  Chapel ;  at 
Peterboro%  in  Our  Lady's  Chapel ;  and  at  Hereford, 
in  the  north  porch.  In  conventual  churches  at 
Windsor,  St.  George's  Chapel  at  Cambridge,  King's 
College  Chapel  at  Westminster,  King  Henry  VII.'s 
Chapel;  at  Great  3Ielverit,  in  Worcestershire,  the 
tower  and  choir;  at  Christ's  Church,  Oxford,  the 
roof  of  the  choir ;  and  at  Evesham  Abbe?/,  in  Worces- 
tershhe,  the  campanile  and  gateway. 

Among  other  principal  examples  in  this  style,  it 
may  be  well  to  mention  that  Scotland  boasts  of  many 
fine  specimens  of  ecclesiastical  architectiure.  The 
Abbeys  of  Melrose  and  Kelso,  founded  by  David  I., 
as  well  as  those  in  Dryburgh  and  Jedburgh,  —  all  in 
Roxbm-ghshire,  —  prove  that  the  art  advanced  to  as 
great  perfection  north  of  the  Tweed  as  it  did  in 
England. 

For  parochial  churches,  except  in  some  very  few 


specimens  in  Somersetsliire,  and  there,  perhaps,  only 
in  parts,  we  are  unable  to  refer  the  reader  to  a  com- 
plete specimen,  in  all  its  parts,  of  the  perpendicular 
style.  The  pulpit  and  screen  at  Dartmouth,  in  Dev- 
onshire, are  worthy  of  his  notice. 

The  following  synoptical  view  of  the  general  di- 
mensions of  the  above  cathedrals,  we  think,  may 
prove  occasionally  useful  to  the  reader,  by  enabling 
him  to  compare  the  whole  of  them  and  their  parts 
with  each  other.  Dallaway,  without  the  remotest 
idea  of  the  principles  in  question,  has  observed, 
with  his  usual  sagacity,  that  there  appears  in  them 
"  a  distribution  of  parts  wiiicli  will  hold  ahnost  gen- 
erally, that  the  width  of  the  nave  is  that  of  both 
the  aisles,  measured  in  the  place  to  the  extremity  of 
the  buttresses  externally ;  and  that  the  breadth  and 
height  of  the  whole  building  arc  equal.  In  the  more 
ancient  churches,  the  aisles  are  usually  of  the  width 
of  the  space  between  the  dividing  arches."  Some 
idea  of  the  principle  is  conveyed  in  the  plates  of 
jNIilan  Cathedral,  curiously  introduced  into  the  very 
early  translation  of  Viti-uvius  by  Ca;sar  Cesarianus, 
a  work  of  great  curiosity,  and  of  which  copies  arc 
now  rarely  met  with. 


A  Synoptical  Vieiv  of  the  leading-  Dimensions  of  the  English  Cathedrals. 


Total 

Cailiedral. 

internal 

Naves  and  Aisle 

J. 

Choirs. 

Transepts. 

Spires  and  Towers. 

Lengtli. 

Length. 

Breadth. 

Height. 

Length. 

Breadth. 

Height. 

Breadth. 

Height. 

Winchester, 

545 

247 

86 

78 

138 



73 

186 

Ely,    . 

517 

327 

73 

70 

101 

73 

70 

178 

Tower,       .        210 

Canterbury, 

514 

214 

70 

80 

150 

74 

80 

154 

Do.,   .        .        235 

Old  St.  Paul's,    . 

500 

a35 

91 

103 

165 

43 

88 

248 

Spire,         .        534 

York,  . 

498 

264 

109 

99 

131 



99 

222 

Tower        .        234 

Lincoln, 

498 

83 

83 



— 

227 

Do.,   .        .        260 

Westminster, 

489 

130 

96 

101 

152 



151 

189 

Peterboro', . 

480 

231 

78 

78 

138 



78 

203 

Louvre,      .        150 

Salisbury,  . 

452 

246 

76 

84 

140 

— 

84 

210 

Spire,         .        387 

Durham,     . 

420 

— 

— 

117 

33 

71 

176 

Tower,       .        214 

Gloucester, 

420 

174 

84 

67 

140 



86 

144 

Do.,   .        .        225 

Lichfield,    . 

411 

213 

67 

— 

110 



67 

Spire,   258  W.  183 

Norwich,    . 

411 

230 

71 

— 

165 

— 

— 

191 

Do.,    .        .        317 

Worcester, 

410 

212 

78 

— 

126 



74 

130 

Tower,       .        196 

Chichester, 

401 

205 

91 

61 

100 



— 

131 

Spire,         .        267 

Exeter, 

390 

173 

74 

69 

131 



69 

140 

Tower,       .        130 

Wells, 

371 

191 

67 

67 

106 

— 

67 

135 

Do.,    .        .        160 

Hereford,  anct.   . 

370 

144 

68 

68 

105 

— 

64 

140 

Chester,      . 

348 

73 

73 





Tower,       .        127 

Rochester, . 

306 

150 

65 

— 

156 



— 

123 

Spire,         .        156 

Carlisle,      . 

213 

71 

71 

137 

71 



Bath,  . 

210 

136 

72 

78 



— 

126 

Tower,       .        162 

Bristol, 

175 

100 

75 

73 

100 



«__ 

128 

Do.,    .        .        127 

Oxford,       . 

154 

74 

54 

41 

80 

— 

374 

102 

Spire,.        .        184 

140 


GOTHIC    ARCHITECTURE. 


To  the  above  vvc  subjoin  the  correspondent  dimen- 
sions of  the  several  component  parts  of  some  of  tlic 
cathedral  churches  enumerated,  which  we  consider 
useful  to  the  student  as  well  as  the  general  reader. 


Total  Length. 

Feet. 

Chichester  cathedral  church, 

, 

410 

Norwich  cathedral  church. 

. 

.     411 

Worcester  cathedral  church, 

. 

410 

Durham  cathedral  church. 

, 

.    420 

Gloucester  conventual  church, 

• 

420 

Ucighls  of  Naves.                Style. 

Feet 

Salisbury  cathedral  church, 

.  84 

Pointed  arch. 

Lincoln  cathedral  church, . 

.  83 

Pointed  arch. 

Canterbury  cathedral  churcli. 

.  80 

Pure  Gothic. 

Peterboro'  conventual  church, 

.  78 

Norman. 

Winchester  cathedi-al  chm-ch, 

.  78 

Pure  Gothic. 

Durham  cathedral  church, . 

.  71 

Norman. 

Ely  cathedral  chm'ch. 

.  70 

Norman. 

Exeter  cathedral  church,    . 

.  69 

Pointed  arch. 

Gloucester  conventual  church, 

.  G7 

Norman. 

Wells  cathedral  church. 

.  67 

Pointed  arch. 

Breadths  of  Naves 

and  Aisles. 

Feet 

Feet. 

Feet. 

Noi-wlch,     .  71       Exeter,    . 

.  74 

Durham,  .     80 

Bristol,    .     .  73       Salisbmy, 

.  76 

Lincoln,   .     83 

Chester,  .     .  73       Peterboro', 

.  78 

Gloucester,    84 

Ely,    ...  73       Worcester, 

.  78 

Winchester,  85 

Canterbury,  74 

The  author  just  quoted,  in  reference  to  the  tables 
here  given,  says  of  them,  that  "the  parallel  will 
afford  VTs,  at  one  view,  authentic  information  con- 
cerning the  proportion  of  one  constituent  part  to 
another  of  every  cathedral  in  England  which  is  wor- 
thy the  notice  of  an  architect.  Such,"  he  continues, 
"  a  coincidence  of  dimensions  as  that  which  is  found 
in  many  of  tlicm  can  scarcely  be  supposed  to  be  the 
effect  of  chance,  especially  where  the  buildings  are 
contemporary,  and  of  an  exactly  correspondent  style." 
It  appears  that  the  equality  of  proportions  is  con- 
fined to  each  era  and  style  of  ecclesiastical  architect- 
ure in  so  remarkable  a  degree  as  to  lead  us  to  con- 
jecture that  they  might  have  been  designed  by  the 
same  architect.  "  The  constant  rivalry,"  says  Dalla- 
way,  "which  subsisted  between  the  magnificent  prel- 
ates, was  excited  upon  the  erection  of  any  part  of  a 


cathedral  of  superior  beauty,  and  imitated  in  those 
of  the  same  kind  which  were  then  undertaken  ;  and 
the  architect  who  had  once  displayed  great  talents 
was  invited  to  repeat  the  more  perfect  performance 
upon  which  he  had  rested  his  professional  fame." 
We  have  not  considered  it  necessary  to  devote  a 
special  portion  of  our  work  to  the  conventual  archi- 
tecture of  England,  because  it  followed  the  style  of 
the  time.  It  was  of  great  splendor.  The  ground 
plans  of  their  habitable  portions  were  usually,  though 
not  always,  quackangular,  and  in  the  later  ages  par- 
took of  the  improvements  in  domestic  architecture, 
as  in  the  colleges  built  by  Wykham  and  Waynflete, 
and  many  of  the  episcopal  residences.  Glastonbury 
and  Reading  presented  exceedingly  fine  examples  of 
it ;  the  former  comprised  within  its  walls  sixty  acres 
of  gi'ound. 

We  have  thus  given,  although  very  briefly,  an  ac- 
count of  the  rise  and  progi'css  of  a  species  of  archi- 
tecture which  is  in  itself  a  wonder,  and  which  has  set 
up  an  eternal  defiance  to  him  who  would  speak  light- 
ly of  the  deep  conception  it  develops,  or  the  wonder- 
ful fertility  of  the  inventive  genius  it  demonstrates. 
It  was  the  production  of  a  peculiar  age,  and,  true  to 
its  time,  it  mirrors  in  every  case  a  transcript  of  the 
mind  of  him  who  conceived  it.  The  low  roof  of  the 
Indian  Temple  of  Elephanta,  or  the  Egyptian  Phila; 
or  Edfu,  were  lofty  enough  for  their  deities.  The 
Parthenon  and  the  Erectheum  of  classic  Greece  were 
sufficiently  spacious  and  significant  of  the  gods  they 
worshipped ;  but  to  the  mind  of  the  Christian,  whose 
vision  extended  beyond  the  confines  of  temples  that 
were  made  with  hands,  the  most  gorgeous  temple  of 
Grecian  story,  although  composed  of  the  purest  mar- 
ble and  of  the  most  classic  design,  was  but  mean  and 
grovelling.  Their  religion  was  of  a.  loftier  nature, 
and  their  aspirations  could  only  be  satisfied  when, 
with  awful  sublimity,  they  saw  the  spire  of  Salisbury 
towering  in  majestic  significance  for  four  hundred 
feet  in  the  air.  In  that  huge  pile,  awful  yet  majestic, 
they  recognized  a  divinity,  the  colossal  grandeur  of 
which  awakened  and  perpetuated  in  their  bosoma 
emotions  of  adoration  and  praise.  Beneath  the  sky 
of  ancient  Rome  stands  one  of  the  seven  wonders  of 
the  world  ;  and,  beneath  that  of  London,  the  glory  of 
Roman  architecture  on  the  soil  of  Old  England.  But 
in  constructing  the  Cathedral  Churches  of  St.  Peter's 
and  St.  Paul's,  the  conception  of  Raphael,  and  An- 


I'l.'i. 


Kl.v.ili,.ii  iin.l   S.-,li..ii  ..r  llir   (  111.  I  M'm.li."  Ill  111.-  .  Mir-.iii.  .■  -^-ili-vi-av. 


i'i.;i;i 


.  yi  ^ii  aavW'.aji/ii.  STTOIKlfu 


I'l.Klil 


I'l.ll' 


GOTHIC    ARCHITECTURE, 


141 


gelo,  and  Wren  were  trammelled  by  the  rules  and 
proportions  of  an  order,  and  a  Roman  sternness 
characterizes  each  pile.  Li  these  is  seen,  it  is  true, 
the  great  victory  that  science  and  skill  have  won  over 
disorder  and  ignorance,  but  in  Gloucester  and  Win- 
chester the  very  essence  of  art  and  ideality.  The 
perfect  columniations  and  nicely-arranged  entabla- 
tures of  the  former  speak  to  us,  it  is  true,  with  a  bold- 
ness that  well  becomes  the  Roman ;  but  the  flowing 
tracery  and  lofty  arches  of  the  latter  breathe  an  air 
of  poctiy :  while  the  gTcat  domes  of  the  one  fill  the 
mind  with  majesty  and  awe,  the  towering  spires  of 
the  others  address  their  solemn  eloquence  to  the  soul. 
We  would  not  underrate  the  talent  which  produced 
the  great  realities  we  place  in  contrast ;  we  give  them 
the  glory  which  a  matured  science  and  a  ripe  skill 
have  hung  around  them  ;  but  we  claim  for  the  others 
that  each  conception  is  distinctly  identified  with  the 
time  which  gave  it  bu-th,  and  that  they  were  the  out- 
gushings  of  souls  who  were  striving  to  gain  the  mas- 
tery over  darkness  and  degradation,  and  whose  lof- 
tiest aspkations  were  the  establishment  and  perpetuity 
of  a  reformed  religion ;  that  they  are  the  mementoes 
of  a  genius  and  invention  which  were  lent  to  a  peo- 
ple who  had  been  appointed  to  assist  at  an  important 
era  in  a  reform  which  is  to  ultimately  rid  the  race  of 
their  vices  and  transgressions.  It  is  to  be  acknowl- 
edged that  the  means  made  use  of  by  the  clergy  were 
often  censurable,  and  at  variance  with  Lhe  principles 
of  the  religion  they  would  inculcate ;  but,  notwith- 
standing all  this,  behind  the  definite  and  sharp 
scientific  outlines  with  which  the  reason  and  expe- 
rience of  six  centuries  have  bouirded  the  dominion 
of  religious  duty,  we  see  standing  out  fi-om  it  all  a 
detertnination  and  an  accomplishment ;  an  intense 
desire,  amounting  in  itself  to  a  demand,  for  a  deeper 


reverence  for  the  principles  of  religion,  as  they  under- 
stood tlicm,and  now,  after  sLx  centuries  have  elapsed, 
the  crowded  aisles  of  a  hundred  cathedrals  speak  out 
their  triumph  and  success,  and  the  walls  which  en- 
close them  are  but  votive  monuments  of  the  immen- 
sity of  their  wonderful  genius.  —  Editors. 

Plates  9§,  99,  100,  101. 

On  these  plates  we  have  given  examples  of  Gothic 
architecture,  with  their  details.  These  plates  are 
transcripts  of  the  examples  they  arc  designed  to  rep- 
resent, and  are  taken  fi-om  Pugin's  Gothic  Architect- 
ure, with  the  figures  and  scale  annexed.  They  are 
not  inserted  as  illustrations  of  cither  of  the  styles  we 
have  described,  neither  do  we  give  them  as  elements 
of  those  styles,  for  did  we  attempt  to  illustrate  each 
style  in  a  manner  that  would  do  justice  to  the  stu- 
dent, some  twelve  plates,  at  least,  would  be  required 
to  give  him  even  a  limited  knowledge  of  the  arches, 
doors,  windows,  and  columns  belonging  to  each  style ; 
and  to  continue  the  illustration  by  examples  of  roofs, 
ceilings,  mouldings,  &c.,  &c.,  all  of  which  would  be 
demanded,  twice  that  number  would  be  reqiiired  in 
addition ;  and  as  it  was  not  the  original  design  of  the 
work  to  treat  upon  this  part  of  the  science,  we  have 
contented  ourselves  with  giving  our  patrons  a  descrip- 
tion of  the  principal  elements  which  compose  it,  and 
would  refer  them,  in  addition  to  the  works  we  have 
named,  to  Rickman's  Gothic  Ai'chitecture,  and  also 
to  the  publications  of  Britton  and  Pugin. 

The  four  plates  alluded  to  contain  so  great  a  va- 
riety of  useful  and  practical  information  for  the  coun- 
try artisan,  or  to  those  who  do  not  have  access  to  the 
works  to  which  we  refer  them,  (and  for  those  our 
whole  work  is  principally  designed,)  that  we  have  been 
induced  to  place  them  in  our  edition.  —  Editors. 


142 


BUILDING. 


BUILDING. 


Aldrich  tcUs  us  that,  in  choosing  a  situation  for  building,  its  vicin- 
ity to  public  edifices  should  be  principally  attended  to  j  that  is,  we 
should  build  as  near  as  convenient  to  the  place  Tvliere  the  business 
of  the  o-micr  chiefly  calls  him.  "  Every  one  would  -ivish  to  be  near 
a  church,"  (or,  perhaps,  should  wish  to  be  so,)  "  but  especially  a 
priest ;  the  la-\\-yer  near  the  hall  of  justice  ;  the  merchant  near  the 
exchange  ;  the  trader  in  the  principal  street ;  and  every  other  citi- 
zen, in  the  same  manner,  •n-ould  choose  his  dwelling  according  to  his 
occupation  —  not  far  from  the  river,  if  any  flow  near  the  city  ;  at  a 
distance  from  a  tallow  chandler,  a  brewer,  a  soap  boiler,  or  any  other 
business  attended  with  an  unsavory  smell ;  far  from  the  noise  of  the 
anvil,  the  hammer,  and  the  saw  ;  and,  above  aU,  (as  Cato  says,)  at  a 
distance  from  bad  neighbors.  In  short,  that  spot  is  most  eligible  in 
which  you  can  construct  a  regular  house  ;  that  is,  one  with  right 
angles  —  where  room,  leisure,  and  cleanliness  may  be  obtained,  and 
you  may  procure  to  your  house  the  advantages  of  a  rural  situation. 
If  all  the  above  conveniences  cannot  be  met  >vith,  (and  it  is  very 
seldom,  if  desired,  that  they  can  be,)  it  is  prudent  to  aim  at  such  as 
may  be  desirable  and  are  attainable. 


Under  this  general  term,  which  implies  the  con- 
struction of  an  edifice,  according  to  the  rules  laid 
down  by  the  different  artificers  employed,  we  purpose 
to  treat  of  the  respective  business  of  the  mason,  brick- 
layer, plasterer,  slater,  plumber,  painter,  and  glazier ; 
previous  to  which  it  will  be  necessary  to  consider  the 
sinking  of  the  foundation,  the  due  mixture  of  the  in- 
gredients which  compose  the  mortar,  and  the  art  of 
making  bricks,  upon  the  whole  of  which  materially 
depends  the  stability  of  an  edifice. 

As  firmness  of  foundation  is  indispensable,  wher- 
ever it  is  intended  to  erect  a  building,  the  earth  must 
be  pierced  by  an  non  bar,  or  stuck  with  a  rammer, 
and,  if  found  to  shake,  must  be  bored  with  a  well- 
sinker's  implement,  in  order  to  ascertain  whether  the 
shake  be  local  or  general.  If  the  soil  is  in  general 
good,  the  loose  and  soft  parts,  if  not  very  deep,  must 
be  excavated  until  the  laborers  arrive  at  a  solid  bed 
capable  of  sustaining  the  pier  or  piers  to  be  built. 
If  not  very  loose,  it  may  be  made  good  by  ramming 
into  it  very  large  stones,  packed  close  together,  and 
of  a  breadth  proportionate  to  the  intended  weight 
of  the  building  ;  but  where  very  bad,  it  must  be  piled 
and  planked. 

In  places  where  the  soil  is  loose  to  any  great  depth, 
and  over  which  it  is  intended  to  place  apertures,  such 
as  doors,  windows,  &c.,  while  the  parts  on  which  the 


piers  are  to  stand  are  firm,  the  best  plan  is  to  turn  an 
inverted  arch  under  each  intended  aperture,  as  then 
the  piers,  in  sinking,  will  carry  with  them  the  inverted 
arch,  and,  by  compressing  the  gi'ound,  compel  it  to 
act  against  the  under  sides  of  the  arch,  which,  if 
closely  jointed,  so  far  from  yielding,  will,  with  the 
abutting  piers,  operate  as  one  solid  body ;  but,  on 
the  contrary,  if  this  expedient  of  the  inverted  arch  is 
not  adopted,  the  part  of  the  wall  under  the  aperture, 
being  of  less  height,  and,  consequently,  of  less  weight 
than  the  piers,  will  give  way  to  the  resistance  of  the 
soil  acting  on  its  base,  and  not  only  injure  the  brick 
work  between  the  apertures,  but  fracture  the  window 
heads  and  sills. 

In  constructing  so  essential  a  part  as  the  arch, 
great  attention  must  be  paid  to  its  curvature,  and 
we  strongly  recommend  the  parabolic  curve  to  be 
adopted,  as  the  most  effectual  for  the  purpose ;  but 
if,  in  consequence  of  its  depth,  this  cannot  conven- 
iently be  introduced,  the  arch  should  never  be  made 
less  than  a  semicircle.  The  bed  of  the  piers  should 
be  as  uniform  as  possible  ;  for  though  the  bottom  of 
the  trench  be  very  firm,  it  will,  in  some  degree,  yield 
to  the  great  weight  that  is  upon  it,  and  if  the  soil  be 
softer  in  one  part  than  in  another,  that  part  which  is 
the  softest  wUl,  of  course,  yield  more  to  the  pressure, 
and  cause  a  fracture. 

K  the  solid  parts  of  the  trench  happen  to  be  under 
the  intended  apertures,  and  the  softer  parts  where 
piers  are  wanted,  the  reverse  of  the  above  practice 
must  be  resorted  to  ;  that  is,  the  piers  must  be  buUt 
on  the  firm  jjarts,  and  have  an  arch  that  is  not  in- 
verted between  them.  In  performing  this,  attention 
must  be  paid  to  ascertain  whether  the  pier  will  cover 
the  arch ;  for  if  the  middle  of  the  pier  rest  over  the 
middle  of  the  summit  of  the  arch,  the  narrower  the 
pier  is  the  gi-eater  should  be  the  ciu'vature  of  the  arch 
at  its  apex.  When  suspended  arches  are  used,  the 
intrados  ought  to  be  kept  clear  of  the  ground,  that 
the  arch  may  have  its  due  effect. 

When  the  gi'ound  is  in  such  a  state  as  to  require 
the  foundation  merely  to  be  rammed,  the  stones  are 
hammer  dressed,  so  as  to  be  of  as  little  taper  as  possi- 
ble, then  laid  of  a  breadth  proportioned  to  the  weight 


BUILDING. 


143 


that  is  to  be  rested  upon  them,  and  afterwards  well 
rammed  together.  In  general,  the  lower  bed  of 
stones  may  be  allowed  to  project  about  a  foot  from 
the  face  of  the  wall  on  each  side,  and  on  this  bed 
another  com-se  may  be  laid,  to  bring  the  bed  of 
stones  on  a  level  with  the  top  of  the  trench.  The 
breadth  of  this  upper  bed  of  stones  should  be  four 
inches  less  than  the  lower  one ;  that  is,  projecting 
about  eight  inches  on  either  side  of  the  wall.  In  all 
kinds  of  walling,  each  joint  of  every  coiu'se  must 
fall  as  nearly  as  possible  in  the  centre,  between  two 
joints  of  the  course  immediately  below  it ;  for,  in  all 
the  various  methods  of  laying  stones  or  bricks,  the 
principal  aim  is  to  procure  the  greatest  lap  on  each 
other. 


MORTAR. 

Li  making  mortar,  particular  attention  must  be 
paid  to  the  quality  of  the  sand,  and  if  it  contain 
any  proportion  of  clay  or  mud,  or  is  brought  fi.-om 
the  sea-shore,  and  contains  saline  particles,  it  must 
be  washed  in  a  stream  of  clear  water  till  it  be  di- 
vested of  its  impiuities.  The  necessity  of  the  fii-st 
has  been  clearly  proved  by  Mr.  Smeaton,  who,  in  the 
course  of  a  long  and  meritorious  attention  to  his 
profession  as  an  engineer,  has  found  that  when  mor- 
tar, though  otherwise  of  the  best  quality,  is  mixed 
with  a  small  proportion  of  unburnt  clay,  it  never 
acquhes  that  hardness  which,  without  it,  it  would 
have  attained ;  and,  with  respect  to  the  second,  it  is 
evident  that,  so  long  as  the  sand  contains  any  saline 
particles,  it  cannot  become  hard  and  diy.  The 
sharper  and  coarser  the  sand  is,  the  better  for  the 
mortar,  and  the  less  the  quantity  of  lime  to  be  used ; 
and  sand  being  the  cheapest  of  the  ingredients  which 
compose  the  mortar,  it  is  more  profitable  to  the 
maker.  The  exact  proportions  of  lime  and  sand  are 
still  undetermined ;  but  in  general,  no  more  lime  is 
required  than  is  just  sufficient  to  surround  the  parti- 
cles of  the  sand,  or  sufficient  to  preserve  the  neces- 
sary degree  of  plasticity. 

Mortar,  in  which  sand  forms  the  gi-eater  portion, 
requires  less  water  in  its  preparation,  and,  conse- 
quently, is  sooner  set.  It  is  also  harder  and  less  lia- 
ble to  shrink  in  drying,  because  the  lime,  while  dry- 
ing, has  a  greater  tendency  to  shrink  than  sand, 
which  retains  its  original  magnitude.     The  general 


proportions  given  by  the  London  buUdcrs  is  1^  cwt., 
or  37  bushels  of  lime,  to  2^  loads  of  sand ;  but,  if 
proper  measures  be  taken  to  procure  the  best  burnt 
lime  and  the  best  sand,  and  in  tempering  the  mate- 
rials, a  greater  portion  of  sand  may  be  used.  There 
is  scarcely  any  mortar  that  has  the  lime  well  cal- 
cined, and  the  composition  well  beaten,  but  that  will 
be  found  to  require  two  parts  of  sand  to  one  part  of 
unslaked  lime  ;  and  it  is  worthy  of  observation,  that 
the  more  the  mortar  is  beaten,  the  less  proportion  of 
lime  suffices. 

Many  experiments  have  been  made,  with  a  view 
to  obtain  the  most  useful  proportion  of  the  ingre- 
dients, and,  among  the  rest.  Dr.  Higgins  has  given 
the  following :  "  Lime,  newly  slaked,  one  part ;  fine 
sand,  three  parts ;  and  coarse  sand,  four  parts." 

He  also  found  that  one  fourth  of  the  lime  of  bone 
ashes  greatly  improved  the  mortar,  by  giving  it 
tenacity  and  rendering  it  less  liable  to  crack  in  the 
drying. 

It  is  best  to  slake  the  lime  in  small  quantities  as 
required  for  use,  about  a  bushel  at  a  time,  in  order  to 
secm-e  to  the  mortar  such  of  its  qualities  as  would 
evaporate  were  it  allowed  to  remain  slaked  for  a 
length  of  time.  But  if  the  mortar  be  slaked  for 
any  considerable  time  previous  to  being  used,  it 
should  be  kept  covered  up,  and,  when  wanted,  should 
be  rebcaten.  If  care  be  taken  to  secure  it  from  the 
action  of  the  atmosphere,  it  may  thus  remain  covered 
up  for  a  considerable  period,  without  its  strength  be- 
ing in  the  least  affected ;  and,  indeed,  some  advan- 
tages are  gained,  for  it  sets  sooner,  is  less  liable  to 
crack  in  the  drying,  and  is  harder  when  dry. 

Grout,  wloich  is  a  cement  containing  a  larger  pro- 
portion of  water  than  the  common  mortar,  is  used  to 
run  into  the  narrow  interstices  and  irregular  courses 
of  rubble-stonc  walls ;  and  as  it  is  reqviired  to  con- 
crete in  the  course  of  a  day,  it  is  composed  of  mor- 
tar that  has  been  a  long  time  made  and  thoroughly 
beaten. 

Mortar,  composed  of  pm-e  lime,  sand  and  water, 
may  be  employed  in  the  linings  of  reservoirs  and 
aqueducts,  provided  a  sufficient  time  is  allowed  for  it 
to  dry  before  the  water  is  let  in ;  but  if  a  sufficient 
time  is  not  allowed,  and  the  water  is  admitted  while 
the  mortar  is  wet,  it  will  soon  fall  to  pieces.  There 
are,  however,  certain  ingredients  which  may  be  put 
into  the  common  mortar  to  make  it  set  immediately 
under  the  water ;  or,  if  the  quicklime  composing  the 


144 


BUILDING, 


mortar  contains  in  itself  a  certain  portion  of  burnt 
clay,  it  wUl  possess  this  property.  For  further  in- 
formation on  this  head,  the  reader  is  referred  to  the 
sub-head  —  Plasterinff. 


MASONRY. 

Masonry  is  the  art  of  cutting  stones,  and  building 
them  into  a  mass,  so  as  to  form  the  regular  sur- 
faces which  arc  requu-ed  in  the  construction  of  an 
edifice. 

The  chief  business  of  the  mason  is  to  prepare  the 
stones,  make  the  mortar,  raise  the  wall  with  neces- 
sary breaks,  projections,  arches,  apertures,  &c.,  as  in- 
dicated by  the  design. 

A  wall  built  of  unhewn  stone,  whether  it  be  built 
with  mortar  or  otherwise,  is  called  a  rubble  jvall. 
Rubble  worlv  is  of  two  kinds,  coursed  and  uncoursed. 
In  coursed  rubble,  the  stones  are  gauged  and  di-cssed 
by  the  hammer,  and  thrown  into  different  heaps,  each 
heap  containing  stones  of  equal  thickness;  and  the 
masonry,  which  may  be  of  different  thicknesses,  is 
laid  in  horizontal  com'ses.  In  uncom-sed  rubble,  the 
stones  are  placed  promiscuously  in  the  wall,  with- 
out any  attention  being  paid  to  arrange  them  in 
courses ;  and  the  only  preparation  the  stones  under- 
go is  that  of  knocking  off  the  sharp  angles  with  the 
thick  end  of  a  tool  called  a  scabling  hammer.  Walls 
are  often  built  with  an  ashlar  facing  of  fine  stone, 
averaging  about  fom-  or  five  inches  m  thickness,  and 
backed  with  rubble  work  or  brick. 

Walls  backed  with  brick  or  uncoursed  rubble  are 
liable  to  become  convex  on  the  outside,  from  the 
great  number  of  joints,  and  the  difficulty  of  placing 
the  mortar,  which  shrinks  in  proportion  to  the  quan- 
tity, in  equal  portions,  in  each  joint ;  consequently, 
walls  of  this  description  are  much  inferior  to  those 
where  the  facing  and  backing  are  built  of  the  same 
material,  and  with  equal  care,  even  though  both  of 
the  sides  be  uncoursed.  When  the  outside  of  a  wall 
is  faced  with  ashlar,  and  the  inside  is  coursed  rubble, 
the  courses  of  the  backing  should  be  as  high  as  pos- 
sible, and  set  within  beds  of  mortar.  Coursed  rub- 
ble and  brick  backings  are  favorable  for  the  insertion 
of  bond  timber ;  but  in  good  masonry,  wooden 
bonds  should  never  be  in  continued  lengths,  as,  in 
case  of  cither  fire  or  rot,  the  wood  will  perish,  and 


the  masonry  will,  by  being  reduced,  be  liable  to  bend 
at  the  place  where  the  bond  was  inserted. 

When  timber  is  to  be  inserted  into  walls  for  the 
purposes  of  fastening  buttons  for  plastering  or  skirt- 
ing, (kc,  the  pieces  of  timber  ought  to  be  so  disposed 
that  the  ends  of  the  pieces  be  in  a  line  with  the  wall. 

In  a  wall  faced  with  ashlar,  the  stones  are  gen- 
erally about  2  feet  or  2i  feet  in  length,  12  inches  in 
height,  and  8  inches  in  thickness.  It  is  a  very  good 
plan  to  incline  the  back  of  each  stone,  to  make  all 
the  backs  thus  inclined  run  in  the  same  direction, 
which  gives  a  small  degree  of  lap  in  the  setting  of 
the  next  course ;  whereas,  if  the  backs  arc  parallel  to 
the  front,  there  can  be  no  lap  where  the  stones  run 
of  an  equal  depth  in  the  thickness  of  the  waU.  It  is 
also  advantageous  to  the  stability  of  the  wall  to  se- 
lect the  stones,  so  that  a  thicker  and  a  thinner  one 
may  succeed  each  other  alternately.  In  each  course 
of  ashlar  facing,  cither  with  rubble  masonry  or  brick 
backing,  thorough  stones  should  occasionally  be  in- 
troduced, and  their  number  be  in  proportion  to  the 
length  of  the  course.  In  every  succeeding  course, 
the  thorough  stones  should  be  placed  in  the  middle 
of  every  two  thorough  stones  in  the  course  below; 
and  this  disposition  of  bonds  should  be  punctually 
attended  to  in  all  cases  where  the  courses  are  of  any 
great  length.  Some  masons,  in  order  to  prove  that 
they  have  introduced  sufficient  bonds  into  their  work, 
choose  thorovigh  stones  of  a  greater  length  than  the 
thickness  of  the  wall,  and  afterwards  cut  off  the  ends ; 
but  this  is  far  from  an  eligible  plan,  as  the  wall  is  not 
only  subject  to  be  shaken,  but  the  stone  is  itself  apt 
to  split.  In  every  pier,  between  windows  and  other 
apertures,  every  alternate  jamb  stone  ought  to  go 
through  the  wall  with  its  bed  perfectly  level.  When 
the  jamb  stones  are  of  one  entire  height,  as  is  fre- 
quently the  case  when  architraves  are  ^\Tougllt  upon 
them,  upon  the  lintel  crowning  them,  and  upon  the 
stones  at  the  ends  of  the  courses  of  the  pier  which 
are  adjacent  to  the  architrave  jamb,  every  alternate 
stone  ought  to  be  a  thorough  stone :  and  if  the  piers 
between  the  apertures  be  very  narrow,  no  other  bond 
stone  is  required ;  but  where  the  piers  arc  wide,  the 
number  of  bond  stones  are  proportioned  to  the  space. 
Bond  stones  must  be  particularly  attended  to  in  all 
long  courses  below  and  above  windows. 

Iron  clamps  are  now  used  in  all  cases  where  it  is 
practicable,  instead  of  thorough  stones.  The  shrink- 
ing of  the  mortar  in  the  backing  is  very  apt  to  start 


BUILDING. 


145 


the  thorough  stone  from  its  true  position,  which  either 
fractures  it,  or  causes  the  wall  to  bulge,  and  open  the 
seams  on  the  outside.  This  inconvenience  is  obvi- 
ated by  the  use  of  clamps. 

All  vertical  joints,  after  receding  about  an  inch 
with  a  close  joint,  should  widen  gradually  to  the 
back,  thereby  forming  hollow  spaces  of  a  wedge-like 
figure  for  the  reception  of  mortar,  rubble,  &c.  The 
adjoinmg  stones  should  have  their  beds  and  vertical 
joints  filled  from  the  face  about  three  quarters  of  an 
inch  inwards,  with  oil  putty,  and  the  rest  of  the  beds 
must  be  fiUed  with  well-tempered  mortar.  Putty 
cement  will  stand  longer  than  most  stones,  and  will 
even  remain  permanent  when  the  stone  itself  is  mu- 
tilated. All  walls  cemented  with  oU  putty,  at  first 
look  unsightly ;  but  this  disagreeable  effect  ceases  in 
a  year  or  less,  when,  if  care  has  been  taken  to  make 
the  color  of  the  putty  suitable  to  that  of  the  stone, 
the  joints  will  hardly  be  perceptible. 

In  selecting  ashlar,  the  mason  should  take  care  that 
each  stone  invariably  lays  on  its  natural  bed,  as,  from 
carelessness  in  this  particular,  the  stones  frequently 
flush  at  the  joints,  and  sooner  admit  the  corrosive 
power  of  the  atmosphere  to  take  effect. 

It  ought  also  to  be  observed,  that,  in  building  walls 
or  insulated  piUars  of  small  horizontal  dimensions, 
every  stone  should  have  its  bed  perfectly  level,  and 
be  without  any  concavity  in  the  middle ;  because,  if 
the  beds  are  concave,  the  joints  wUl  most  probably 
flush  when  the  piUars  begin  to  sustain  the  weight  of 
the  building.  Care  should  also  be  taken  that  every 
course  of  masonry  in  such  piers  be  of  one  stone. 

Having  thus  given  to  the  practical  mason  an  out- 
line of  the  subject  of  walling,  we  will  proceed  to  the 
consideration  of  the  more  difficult  branches  of  the 
art  —  that  of  constructing  arches  and  vaults. 

DEFINITIONS. 

An  arch,  in  masonry,  is  that  part  of  a  building 
which  is  suspended  over  a  given  plane,  supported 
only  at  its  extremities,  and  concave  towards  tlie  plane. 

The  upper  surface  of  an  arch  is  called  the  extrados ; 
and  the  under  surface,  or  that  which  is  opposite  the 
plane,  the  intrados. 

The  supports  of  an  arch  are  called  the  spring  ivalls. 

The  spring-ing  lines  are  those  common  to  the  sup- 
ports and  the  intrados,  or  the  line  which  forms  the 
intersection  of  the  arch  with  the  surface  of  the  wall 
which  supports  it. 

19 


The  chord  or  span  is  a  line  extending  from  one 
springing  line  to  the  opposite  one. 

Section  of  the  hollow  of  the  arch  is  a  vertical  plane, 
supposed  to  be  contained  by  the  span  and  the  in- 
trados. 

The  height  or  rise  of  the  arch  is  a  line  drawn  at 
right  angles  from  the  middle  of  the  chord,  or  span- 
ning line,  to  the  intrados. 

The  croivn  of  the  arch  is  that  part  which  the  ex- 
tremity of  the  perpendicular  touches. 

The  haunches  or  flanks  of  the  arch  are  those  parts 
of  the  curve  between  the  crown  and  the  springing  line. 

When  the  base  of  the  section,  or  spanning  line,  is 
parallel  to  the  horizon,  the  section  will  consist  of  two 
equal  and  similar  parts,  so  that,  when  one  is  applied 
to  the  other,  they  will  be  found  to  coincide. 

Arches  are  variously  named,  according  to  the  fig- 
ure of  the  section  of  a  solid  that  would  fill  the  void, 
as  circular,  elliptical,  cycloidal,  catenarian,  parabolical, 
&c.  There  are  also  pointed,  composite,  and  lancet  or 
Gothic  arches. 

A  rampant  arch  is  when  the  springing  lines  are  of 
two  unequal  heights. 

When  the  intrados  and  extrados  of  an  arch  are 
parallel,  it  is  said  to  be  extradossed. 

There  are,  however,  other  terms  much  used  by  ma- 
sons :  for  example,  the  semicircular  are  called  perfect 
arches;  and  those  less  than  a  semicircle,  imperfect, 
surbused,  or  diminished  arches. 

Arches  are  called  stilted  when  they  are  higher  than 
a  semicircle. 

A  vault  is  an  arch  used  in  the  interior  of  a  build- 
ing, overtopping  an  area  of  a  given  bomidary,  as  a 
passage,  or  an  apartment,  and  supported  by  one  or 
more  walls,  or  pillars,  placed  without  the  boundary 
of  that  area. 

Hence  an  arch  in  a  wall  is  seldom  or  never  called 
a  vault ;  and  every  vault  may  be  called  an  arch,  but 
every  arch  cannot  be  termed  a  vault. 

A  groin  vault  is  a  complex  vault,  formed  by  the 
intersection  of  two  solids,  whose  surfaces  coincide 
with  the  intrados  of  the  arches,  and  are  not  confined 
to  the  same  heights.  An  arch  is  said  to  stand  upon 
splayed  jambs  when  the  springing  lines  are  not  at 
right  angles  to  the  face  of  the  wall. 

In  the  art  of  constructing  arches  and  vaults,  it  is 
necessary  to  bmld  them  in  a  mould,  until  the  whole 
is  closed ;  the  mould  used  for  this  purpose  is  called 
a  centre. 


146 


BUILDING. 


The  intrados  of  a  simple  vault  is  generally  formed 
of  a  portion  of  a  cylinder,  cylindroid,  sphere,  or  sphe- 
roid ;  that  is,  never  greater  than  the  half  of  the  solid ; 
and  the  springing  lines  which  terminate  the  walls, 
or  when  the  vault  begins  to  rise,  are  generally  straight 
lines,  parallel  to  the  axis  of  the  cylinder  or  cylindroid. 

A  circular  wall  is  generally  terminated  with  a 
spherical  vault,  which  is  either  hemispherical,  or  a 
portion  of  a  sphere  less  than  a  hemisphere. 

Every  vault  which  has  a  horizontal,  straight  axis 
is  called  a  straight  vault;  and,  in  addition  to  what 
we  have  ab-eady  said,  the  concavities  which  two  sol- 
ids form  at  an  angle  receive  likewise  the  name  of 
arch. 

An  arch,  when  a  cylinder  pierces  another  of  a 
greater  diameter,  is  called  cylindro-cylindric.  The 
term  cylindro  is  applied  to  the  cylinder  of  the  greatest 
diameter,  and  the  term  cylindric  to  the  less. 

If  a  cylinder  intersect  a  sphere  of  greater  diameter 
than  the  cylinder,  the  arch  is  called  a  sphero-cylindric 
arch;  but,  on  the  other  hand,  if  a  sphere  pierce  a 
cylinder  of  greater  diameter  than  the  sphere,  the 
arch  is  called  a  cylindro-spheric  arch. 

If  a  cylinder  pierce  a  cone,  so  as  to  make  a  com- 
plete perforation  through  the  cone,  two  complete 
arches  will  be  formed,  called  cono-cylindric  arches; 
but,  on  the  contrary,  if  a  cone  pierce  a  cylinder  so 
that  the  concavity  made  by  the  cone  is  a  conic  sur- 
face, the  arch  is  called  a  cylindro-conic  arch. 

If ,  in  a  straight  wall,  there  be  a  cylindric  aperture 
continuing  quite  through  it,  two  arches  will  be  formed, 
called  plano-cylindric  arches. 

Every  description  of  arch  is,  in  a  similar  manner 
to  the  above,  denoted  by  the  two  preceding  words  — 
the  former  ending  in  o,  signifying  the  principal  vault, 
or  surface  cut  through  ;  and  the  latter  in  ic,  signify- 
ing the  description  of  the  aperture  which  pierces  or 
intersects  the  wall  or  vault. 

When  groins  are  introduced  merely  for  use,  they 
may  be  built  either  of  brick  or  stone ;  but,  when  in- 
troduced by  way  of  proportion  or  decoration,  their 
beauty  will  depend  on  the  generating  figures  of  the 
sides,  the  regularity  of  the  surface,  and  the  acuteness 
of  the  angles,  which  should  not  be  obtruded.  In  the 
best  buildings,  when  durability  and  elegance  are 
equally  required,  they  may  be  constructed  of  wrought 
stone ;  and,  when  elegance  is  wanted,  at  a  trifling 
expense,  of  plaster,  supported  by  timber  ribs. 

In  stonecutting,   a   narrow  surface  formed  by  a 


point  or  chisel   on  the  surface  of  a  stone,  so  a#  to 
coincide  with  a  straight  edge,  is  called  a  draught. 

FORMATION  OF  STONE  ABCHES. 

The  formation  of  stone  arches  has  always  been 
considered  a  most  useful  and  important  acquisition 
to  the  operative  mason  ;  in  order,  therefore,  to  remove 
any  difficulties  which  might  arise  in  the  construction 
of  arches  of  different  descriptions,  both  in  straight 
and  circular  walls,  we  shall  here  introduce  a  few  ex- 
amples, which,  it  is  hoped,  with  careful  examination, 
will  greatly  facilitate  a  knowledge  of  some  of  the 
most  abstruse  parts  of  the  art. 

Plate  102. 

To  find  the  moulds  necessary  for  the  construc- 
tion of  a  semicircular  arch,  cutting  a  straight 
wall  obliquely. 

Fig.  1,  No.  1.  Let  A  B  C  D  E  F  G  H  be  the  plan 
of  the  arch ;  I  K  L  M  the  outer  line  ;  and  N  O  P  Q 
the  inner  line  on  the  elevation. 

a  b  c  d  e,  on  the  elevation,  shows  the  bevel  of  each 
joint  or  bed  from  the  face  of  the  wall ;  and  a  b  c  d  e, 
below,  gives  the  mould  for  the  same,  where  x  y  on 
the  elevation  corresponds  with  xy  2it  a. 

The  arch  mould,  No.  2,  is  applied  on  the  face  of 
the  stone,  and,  on  being  applied  to  the  parts  of  the 
plan,  gives,  of  course,  the  bevel  of  each  concave  side 
of  the  stone  with  the  face  —  that  is,  K  to  O,  on  the 
elevation. 

To  find  the  mould  for  constructmg  a  semicir- 
cular arch  in  a  circular  wall. 

Fig.  2,  No.  1,  is  the  elevation  of  the  arch,  and  No.  2 
the  plan  of  the  bottom  bed  from  q  to  r. 

a  to  b  is  what  the  arch  gains  on  the  circle  from  the 
bottom  bed  k  o  to  I ;  and  c  to  d  is  the  projection  of 
the  intrados  to  p,  on  the  point  /,  p. 

Nos.  2,  3,  and  4  are  plans  of  the  three  arch  stones, 
1,  2,  3,  in  the  elevation ;  and  Nos.  5  and  6  are  moulds 
to  be  applied  to  the  beds  of  stones  1  and  2,  in  which 
s  c  equals  5  c  in  No.  2,  and  t  to  equals  t  to  in  No.  3. 

In  No.  1,  k  Ip  0  is  the  arch  or  face  mould. 

When  the  reader  is  thoroughly  proficient  in  the 
construction  of  arches  under  given  data,  as  the  cir- 
cumstances of  the  case  may  point  out,  he  may  pro- 
ceed to  investigate  the  principles  of  spherical  domes 
and  groins. 


A(a®rai£3. 


I'l.KU 


« 


I 


I 


BUILDING. 


147 


Figs.  3  and  4  show  the  principles  of  developing 
the  sofRts  of  the  arches  in  the  two  preceding  exam- 
ples. In  each  the  letters  of  reference  are  alike,  and 
the  operation  is  precisely  the  same. 

Let  A  B  D  E  be  the  plan  of  the  opening  in  the 
wall,  and  A  F  B  the  elevation  of  the  arch ;  produce 
the  chord  A  B  to  C,  divide  the  semicurcle  A  F  B  into 
any  number  of  parts,  the  more  the  better,  and  with 
the  compasses  set  to  any  one  of  these  divisions,  run 
it  as  many  times  along  A  C  as  the  semicircle  is 
divided  into ;  then  draw  lines,  perpendicular  to  B  C, 
through  every  division  in  the  semicircle  and  the  line 
C  A,  and  set  the  distance  1  b,  2  d,  3  f,  &c.,  respec- 
tively equal  to  ab  c  d  ef,  &c.,  and  then,  by  tracing  a 
curve  through  these  points  and  finding  the  points  in 
the  line  G  D,  in  the  same  manner,  the  soffit  of  the 
arch  is  complete. 

Fig.  5  shows  the  method  of  constructing  spherical 
domes. 

No.  1  mould  is  applied  on  the  spherical  surface  to 
the  vertical  joints,  and  No.  2  mould  on  the  same 
surface  to  the  other  joints,  and,  in  both  cases,  the 
mould  tends  to  the  centre  of  the  dome. 

3,  4,  5,  6,  7,  and  8  are  moulds  which  apply  on  the 
convex  surface  to  the  horizontal  joint,  the  lines  a  b, 
c  d,  e  f,  &c.,  being  at  right  angles  to  the  different 
radii,  b  c,  d  c,f  c,  &c.,  and  produced  until  they  inter- 
sect the  perpendicular  a  c  ;  the  different  intersections 
are  the  centres  which  give  the  circular  leg  of  the 
mould,  and  the  straiglit  part  gives  the  horizontal 
joint. 

Fig.  6  exhibits  the  plan  of  a  groined  vault. 

Lay  down  the  arch,  either  at  the  full  or  half  size, 
on  a  floor  or  piece  of  floorcloth,  then  divide  and  draw 
on  the  plan  the  number  of  joints  in  the  semicircular 
arch,  and  from  the  intersections  with  the  diagonals 
draw  the  transverse  joints  on  the  plan,  and  produce 
them  tUl  they  touch  the  intrados  of  the  elliptical  arch, 
the  curve  of  which  may  be  found  by  setting  the  cor- 
responding distances  from  the  luie  of  the  base  to  the 
curve  ;  thus  a  b  equal  to  a  b.  This  being  accom- 
plished, di-aw  the  joints  of  the  elliptical  arch  in  the 
manner  of  which  we  give  c  rf  as  a  specimen.  To 
draw  the  joint  c  d,  draw  chord  e  c  and  bisect  it,  draw 
a  line  from  the  centre  c  through  the  bisecting  point, 
and  produce  it  tUl  it  touches  the  perpendicular  ef; 
and  c  d,  being  at  right  angles  to  c  /,  will  be  the  joint 
required.  In  the  same  manner  the  others  are  found. 
By  examination,  it  will  be  seen  that  a  rectangle 


circumscribing  the  mould  3,  3,  gives  the  size  of  the 
stone  in  its  square  state,  and  that,  if  each  stone  in 
both  arches  be  thus  enclosed,  the  dimensions  for 
each  will  be  found,  as  also  the  position  in  which  the 
moulds  must  be  placed.  The  dark  lines  give  the 
different  bevels,  which  must  be  carefully  prepared 
and  applied  to  the  stones  in  the  manner  represented 
in  the  figure. 

To  draw  the  joints  of  the  stones  for  an  elliptical 
arch  in  a  wall,  &c. 

Fig.  7.  The  curve  is  here  described  by  the  inter- 
section of  lines,  which  certainly  gives  the  most  easy 
and  pleasing  curve,  as  segments  of  circles  apply  only 
under  certain  data,  or  in  the  proportion  which  the 
axis  major  has  to  the  axis  minor,  while  the  intersec- 
tion of  lines  apply  to  any  description  of  ellipses. 
Find  the  foci  F.  In  an  ellipsis,  the  distance  of  either 
focus  from  one  extremity  of  the  axis  minor  is  equal 
to  the  semi-axis  major  ;  that  is,  D  F  is  equal  to  c  C. 
Then,  to  find  any  joint,  a  b,  draw  lines  from  both  foci 
through  the  point  b,  as  F  e,  /  d,  and  bisect  the  angle 
d  b  ehy  the  line  a  b,  which  is  the  joint  required. 


BRICKLAYING. 

In  building  upon  an  inclined  plane,  or  rising  ground, 
the  foundation  must  be  made  to  rise  in  a  series  of 
level  steps,  according  to  the  general  rise  of  the  ground, 
to  insure  a  firm  bed  for  the  courses,  and  prevent  them 
from  sliding ;  for  if  this  mode  were  not  adopted,  the 
moisture  in  the  foundations,  in  wet  weather,  will  in- 
duce the  inclined  parts  to  descend,  to  the  manifest 
danger  of  fracturing  the  walls  and  destroying  the 
building. 

Li  walling,  in  dry  weather,  when  the  work  is  re- 
quired to  be  firm,  the  best  mortar  must  be  used,  and 
the  bricks  must  be  wetted  or  dipped  in  water  as  they 
are  laid,  to  cause  them  to  adhere  to  the  mortar,  which 
they  would  not  do  if  laid  dry ;  for  the  dry,  sandy  na- 
ture of  the  brick  absorbs  the  moisture  of  the  mortar, 
and  prevents  adhesion. 

In  carrying  up  the  wall,  not  more  than  four  or  five 
feet  of  any  part  should  be  built  at  a  time ;  for,  as 
all  walls  shrink  immediately  after  building,  the  part 
which  is  first  carried  up  will  settle  before  the  adja- 
cent part  is  carried  up  to  it,  and,  consequently,  the 


148 


BUILDING. 


shrinldng  of  the  latter  will  cause  the  two  parts  to 
separate ;  therefore,  no  part  of  a  wall  should  be  car- 
ried higher  than  one  scaffold,  without  having  its 
contingent  parts  added  to  it.  In  carrying  up  any 
particular  part,  the  ends  should  be  regularly  sloped 
off,  to  receive  the  bond  of  the  adjoining  parts  on  the 
right  and  left. 

There  are  two  kinds  of  bond  in  brick  work,  which 
differ  materially  from  each  other.  Bricks  laid  length- 
wise in  the  direction  of  the  wall  are  called  stretchers, 
and  those  laid  in  an  opposite  way,  crossing  the  direc- 
tion of  the  wall,  are  called  headers.  The  old  English 
bond  is  a  continuation  of  one  Idnd  throughout  in  the 
same  course  or  horizontal  layer,  and  consists  of  alter- 
nate layers  of  headers  and  stretchers  —  the  headers 
serving  to  bind  the  wall  together  in  a  longitudinal 
direction,  or  lengthwise,  the  stretchers  to  prevent 
the  wall  splitting  crosswise,  or  in  a  transverse  direc- 
tion. Of  these  two  evils,  the  former  is  by  much  the 
worst  kind,  and  is,  therefore,  the  most  dreaded  by  the 
bricklayer.  The  brick  work  of  the  Romans  was  of 
this  kind  of  bond. 

The  other  description  of  bond,  called  Flemish  bond, 
consists  in  placing  a  header  and  a  stretcher  alternately 
in  the  same  course.  The  latter  is  deemed  the  neat- 
est and  most  elegant ;  but,  in  the  execution,  is  at- 
tended with  great  inconvenience,  and,  in  most  cases, 
does  not  unite  the  parts  of  a  wall  with  the  same  de- 
gree of  firmness  as  the  English  bond.  In  general,  it 
may  be  observed,  that  whatever  advantages  are  gained 
by  the  English  bond  in  tying  a  wall  together  in  its 
thickness,  are  lost  in  the  longitudinal  bond,  and  vice 
versa.  To  remove  this  inconvenience  in  thick  walls, 
some  builders  place  the  bricks  in  a  cone  at  an  angle 
of  forty-five  degrees,  parallel  to  each  other,  through- 
out the  length  of  every  course,  but  reversed  in  the 
alternate  courses  ;  so  that  the  bricks  cross  each  other 
at  right  angles.  But  even  here,  though  the  bricks  in 
the  cone  have  sufficient  bond,  the  sides  are  very 
imperfectly  tied,  on  account  of  the  triangular  in- 
terstices formed  by  the  oblique  direction  of  the  in- 
ternal bricks  against  the  fiat  edges  of  those  in  the 
outside. 

Concerning  the  English  bond,  it  may  be  observed, 
that,  as  the  longitudinal  extent  of  a  brick  is  nine 
inches  and  its  breadth  four  and  a  half,  to  prevent  two 
vertical  joints  from  running  over  each  other  at  the 
end  of  the  stretcher  from  the  corner,  it  is  usual,  after 


placing  the  retiu-n  corner  stretcher,  which  occupies 
half  the  length  of  this  stretcher,  and  becomes  a  header 
in  the  face,  as  the  stretcher  is  below,  to  place  a  quar- 
ter brick  on  the  side,  so  that  the  two  together  extend 
six  inches  and  three  quarters,  being  a  lap  of  two 
inches  and  a  half  for  the  next  header.  The  bat  in- 
troduced is  called  a  closer.  A  similar  effect  may  be 
obtained  by  introducing  a  three-quarter  bat  at  the 
corner  of  the  stretching  course,  so  that  the  corner 
header  being  laid  over  it,  a  lap  of  two  inches  and 
a  quarter  will  be  left  at  the  end  of  the  stretch- 
ers below,  for  the  next  header,  which,  being  laid  on 
the  joint  below  the  sti-etchers,  will  coincide  with  its 
middle. 

In  the  winter,  it  is  very  essential  to  keep  the  un- 
finished wall  from  the  alternate  effects  of  rain  and 
frost ;  for,  if  it  is  exposed,  the  rain  will  penetrate  into 
the  bricks  and  mortar,  and,  by  being  converted  into 
ice,  expand,  and  burst  or  crumble  the  materials  in 
which  it  is  contained. 

The  decay  of  buildings,  so  commonly  attributed 
to  the  effect  of  time,  is,  in  fact,  attributable  to  this 
source  ;  but  as  finished  edifices  have  only  a  vertical 
surface,  the  action  and  counteraction  of  the  rain 
and  frost  extend  not  so  rapidly  as  in  an  unfinished 
wall,  where  the  horizontal  surface  permits  the  rain 
and  frost  to  have  easy  access  into  the  body  of  the 
work.  Great  care,  therefore,  must  be  taken,  as  soon 
as  the  frost  or  stormy  weather  sets  in,  to  cover  the 
unfinished  walls  either  with  straw,  which  is  the  most 
common,  or  weather  boarding. 

When  weather  boarding  is  employed,  it  is  advi- 
sable to  have  a  good  layer  of  straw  between  the 
work  and  the  boarding,  and  to  place  the  boarding  in 
the  form  of  stone  coping,  to  throw  the  water  off 
equally  on  both  sides. 

A  number  of  very  pleasing  cornices  and  other 
ornaments  may  be  formed  in  brickwork,  by  the  mere 
disposition  of  the  bricks,  without  cutting;  and  if 
cut,  a  simple  chamfer  will  be  sufficient.  A  great  de- 
fect, however,  is  very  often  observable  in  these  orna- 
ments, particularly  in  the  bulging  of  arches  over 
windows,  which  arises  fi-om  mere  carelessness  in 
rubbing  the  bricks  too  much  on  the  inside  ;  whereas, 
if  due  care  were  taken  to  rub  them  exact  to  the 
gauge,  their  geometrical  bearings  being  united,  they 
would  all  tend  to  one  centre,  and  produce  a  well- 
proportioned  and  pleasing  effect. 


BUILDING. 


149 


PLASTERING. 

The  plasterer  is  a  workman  to  whom  the  decora- 
tive part  of  architecture  owes  a  considerable  portion 
of  its  effect,  and  whose  art  is  requisite  in  every  kind 
of  building. 

The  tools  of  the  plasterer  consist  of  a  spade  or 
shovel  of  the  usual  description ;  a  rake,  with  two  or 
three  prongs  bent  downwards  from  the  line  of  the 
handle,  for  mixing  the  hair  and  mortar  together; 
troicels  of  various  kinds  and  sizes;  stopping'  and 
picking-ont  tools;  rules  called  straight  edges;  and 
wood  models. 

The  trowels  used  by  plasterers  are  more  neatly 
made  than  tools  of  the  same  name  used  by  other 
artificers.  The  laying  and  smoothing  tool  consists  of 
a  flat  piece  of  hardened  iron,  about  ten  inches  in 
length,  and  two  inches  and  a  half  wide,  very  thin, 
and  ground  to  a  semicircular  shape  at  one  end,  but 
left  square  at  the  other ;  and  at  the  back  of  the  plate, 
near  the  square  end,  is  riveted  a  small  iron  rod  with 
two  legs,  one  of  which  is  fixed  to  the  plate,  and  the 
other  to  a  round,  wooden  handle.  With  this  tool  all 
the  first  coats  of  plaster  are  laid  on,  as  is  also  the 
last,  or,  as  it  is  technically  termed,  the  setting.  The 
other  kinds  of  trowels  are  made  of  three  or  four 
sizes,  for  gauging  the  fine  stuff  and  plaster  used  in 
forming  cornices,  mouldings,  &c.  The  longest  size 
of  these  is  about  seven  inches  on  the  plate,  which  is 
of  polished  steel,  about  two  inches  and  three  quar- 
ters broad  at  the  heel,  diverging  gradually  from  a 
point.    To  the  heel  or  broad  end  a  handle  is  adapted. 

The  stopping  and  picking-ont  tools  are  made  of 
polished  steel,  of  different  sizes,  though  most  gener- 
ally about  seven  or  eight  inches  in  length,  and  half 
an  inch  in  breadth,  flattened  at  both  ends,  and  ground 
somewhat  round.  These  tools  are  used  in  modelling 
and  finishing  mitres  and  returns  to  cornices;  as, like- 
wise, in  filling  up,  and  perfecting  the  ornaments  at 
the  jomings. 

The  straight  edges  are  for  keeping  the  work  in  an 
even  or  perpendicular  line  ;  and  the  models  or  moulds 
are  for  running  plain  mouldings,  cornices,  &c. :  of 
these  latter,  the  plasterers  require  a  greater  number, 
as  very  little  of  his  finishing  can  be  done  without 
them. 

Experienced  workmen  keep  their  tools  very  clean, 
and  have  them  daily  polished. 

Plasterers  have  technical  divisions  of  their  work, 


by  which  its  quality  is  designated  and  value  ascer- 
tained; as,  lathing;  laying;  pricking  up;  lathing, 
laying,  and  set;  lathing,  floating,  and  set;  screed, set, 
or  putty ;  rendering  and  set ;  or  rendering,  floated, 
and  set ;  trowelled  stucco,  &c. ;  each  of  which,  here- 
after, we  shall  very  minutely  explain. 

In  all  the  operations  of  plastering,  lime  exten- 
sively abounds ;  we  shall,  therefore,  first  offer  some 
observations  on  the  properties  of  this  important 
article. 

All  who  have  written  on  the  subject  of  lime,  as  a 
cement,  have  endeavored  to  ascertam  what  is  the  due 
proportion  of  sand  for  making  the  most  perfect  cem- 
ent ;  but,  with  a  little  attention,  it  is  evident  that 
aU  prescribed  rules  must  be  so  very  vague  and  un- 
certain, as  to  be  of  little  utility  to  the  workman ;  for, 
besides  the  variation  which  is  occasioned  by  a  more 
or  less  degree  of  calcination,  it  is  a  certain  fact,  that 
some  kinds  of  limestone  are  much  more  pinre,  and 
contain  a  much  smaller  proportion  of  sand,  thaa 
others ;  consequently,  it  would  be  absurd  to  say  that 
pure  lime  requires  as  small  a  proportion  of  sand, 
when  made  into  mortar,  as  that  which  originally 
contained  in  itself  a  large  proportion. 

The  variation  thus  produced,  in  regard  to  the  pro- 
portion of  sand,  is  found  to  be  extremely  great.  It 
is,  however,  stated  that  the  best  mortar  which  has 
come  under  examination  was  formed  of  eleven  parts 
of  sand  to  one  of  lime ;  to  which  was  added,  by 
measure,  between  twice  and  thrice  its  own  bulk  of 
sand,  which  may  be  allowed  to  have  been  at  least 
three  times  its  quantity  by  weight.  Supposing, 
therefore,  that  every  particle  of  the  lime  had  been  so 
perfectly  calcined  as  to  be  in  a  caustic  state,  there 
could  not  be  less  than  forty-seven  parts  of  sand  to 
one  of  lime ;  but  it  is  hard  to  suppose  that  above 
one  hundredth  part  of  this  mass,  independent  of  the 
water,  consisted  of  pure  caustic  calcareous  earth. 

From  these  considerations,  it  is  conceived  that  it 
is  impossible  to  prescribe  any  determinate  proportion 
of  sand  to  lime,  as  that  must  vary  according  to  the 
nature  of  the  lime  and  other  incidental  circum- 
stances, which  would  form  an  infinity  of  exceptions 
to  any  general  rule.  But  it  would  seem  that  it 
might  be  safely  inferred  that  the  moderns,  in  general, 
rather  err  in  giving  too  little,  than  in  giving  too  much, 
sand.  It  deserves,  however,  to  be  noticed,  that  the 
sand,  when  naturally  in  the  limestone,  is  more  inti- 
mately blended  with  the  lime  than  can  possibly  be 


150 


BUILDING. 


ever  effected  by  any  mechanical  operation  ;  so  that  it 
would  be  in  vain  to  hope  to  make  equally  good  mor- 
tar artificially  from  pm-e  lime,  with  so  small  a  pro- 
portion of  caustic  calcareous  matter,  as  may  some- 
times be  effected,  when  the  lime  naturally  contains  a 
very  large  proportion  of  sand.  Still,  however,  there 
seems  to  be  no  doubt,  that  if  a  much  larger  propor- 
tion of  sand  than  is  common  were  employed,  and 
that  more  carefully  and  expeditiously  blended  and 
worked,  the  mortar  would  be  made  much  more  per- 
fect, as  has  been  proved  by  actual  experiments. 

Another  circumstance,  which  greatly  tends  to  vary 
the  quality  of  cement  and  to  make  a  greater  or 
smaller  proportion  of  sand  necessary,  is  the  mode  of 
preparing  the  lime  before  it  is  beaten  up  into  mortar. 
When  for  plaster,  it  is  of  great  importance  to  have 
every  particle  of  the  limestone  slaked  before  it  is 
worked  up  ;  for,  as  smoothness  of  surface  is  the  most 
material  point,  if  any  particles  of  lime  be  beaten  up 
before  sufficiently  slaked,  the  water  still  continuing 
to  act  on  them,  wUl  cause  them  to  expand,  which 
will  produce  those  excrescences  on  the  surface  of  the 
plaster  termed  blisters.  Consequently,  in  order  to 
obtain  a  perfect  kind  of  plaster,  it  is  absolutely  ne- 
cessary that  the  lime,  before  being  worked,  be  allowed 
to  remain  a  considerable  time  macerating  or  souring 
in  water :  the  same  sort  of  process,  though  not  abso- 
lutely required,  would  considerably  improve  the  lime 
intended  for  mortar.  Great  care  is  required  in  the 
management,  the  principal  thing  being  the  procur- 
ing of  well-burnt  lime,  and  allowing  no  more  lime, 
before  worked,  than  is  just  sufficient  to  macerate  or 
sour  it  with  the  water :  the  best-burnt  lime  will  re- 
quire the  maceration  of  some  days. 

It  has  been  almost  universally  admitted,  that  the 
hardest  limestone  affords  the  lime  which  will  consol- 
idate into  the  finest  cement ;  hence,  it  is  generally 
concluded  that  lime  made  of  chalk  produces  a  much 
weaker  cement  than  that  made  of  marble  or  lime- 
stone. It  would  seem,  however,  that,  if  ever  this  be 
the  case,  it  is  only  incidentally,  and  not  necessarily. 
In  making  the  mortar,  other  substances  are  occasion- 
ally mixed  with  lime,  which  wc  shall  here  proceed  to 
notice,  and  endeavor  to  point  out  their  excellences 
and  defects.  Those  commonly  used,  besides  sand 
of  various  denominations,  are  powdered  sandstone, 
brickdust,  and  sea  shells;  and  for  forming  plaster 
where  closeness,  rather  than  hardness,  is  required, 
lime  which  has  been  slaked,  and  kept  in  a  dry  place 


till  it  has  become  nearly  effete,  and  powdered  chalk, 
or  whiting,  and  gypsum,  in  various  proportions,  be- 
sides hair  and  other  materials  of  a  similar  nature. 
Other  ingredients  have  been  more  lately  recom- 
mended, such  as  earthy  balls,  slightly  burnt  and 
pounded,  old  mortar  rubbish,  powdered  and  sifted, 
and  various  things  of  the  like  kind,  the  whole  of 
which   are,  in   some  respect  or  other,  objectionable. 

Plaster  of  Paris  is  employed  by  the  plasterer  to 
give  the  requisite  form  and  finish  to  all  the  superior 
parts  of  his  work.  It  is  made  of  a  fossil  stone 
called  gypsum,  which  is  excavated  in  several  parts 
of  the  neighborhood  of  Paris,  where  it  derives  its 
name,  and  is  calcined  to  a  powder,  to  deprive  it  of 
its  water  of  crystallization. 

The  stones  are  burnt  in  kilns,  which  are  generally 
of  very  simple  construction,  being  not  unfrequently 
buUt  of  .the  gypsum  itself.  The  pieces  to  be  cal- 
cined are  loosely  put  together  in  a  parallelopiped 
heap,  below  which  are  vaulted  pipes  or  flues,  for  the 
application  of  a  moderate  heat. 

The  calcination  must  not  be  carried  to  excess,  as 
otherwise  the  plaster  will  not  form  a  solid  mass  when 
mixed  with  a  certain  portion  of  water.  During  the 
process  of  calcination,  the  water  of  crystallization 
rises  as  white  vapor,  which,  if  the  atmosphere  be  dry, 
is  quickly  dissolved  in  air. 

The  pounding  of  the  calcined  fragments  is  per- 
formed sometimes  in  miUs  constructed  for  the  pur- 
pose, and  sometimes  by  men,  whose  health  is  much 
impaired  by  the  particles  of  dust  settling  upon  their 
lungs. 

On  the  River  Wolga,  in  Russia,  where  the  burning 
of  gypsum  constitutes  one  of  the  chief  occupations 
of  the  peasantry,  all  kinds  of  gypsum  are  burnt  pro- 
miscuously on  grates  made  of  wood  ;  afterwards,  the 
plaster  is  reduced  to  powder,  passed  through  a  sieve, 
and  finally  formed  into  small,  round  cakes,  which  are 
sold  at  so  much  per  thousand. 

These  balls  are  reduced  into  an  impalpable  powder 
by  the  plasterer,  and  then  mixed  with  mortar. 

The  less  the  gypsum  is  mixed  with  other  sub- 
stances, the  better  it  is  qualified  for  the  purpose  of 
making  casts,  stucco,  &c.  The  sparry  gypsum,  or 
selenite,  which  is  the  purer  kind,  is  employed  for 
taking  impressions  from  coins  and  medals,  and  for 
making  those  beautiful  imitations  of  marble,  grahite, 
and  porphyry,  known  by  the  name  of  scagliola,  which 
is  derived  from  the  Italian  word  scagli. 


BUILDING. 


151 


Finely-powdered  alabaster,  or  plaster  of  Paris, 
when  heated  in  a  crucible,  assumes  the  appearance 
of  a  fluid,  by  rolling  in  waves,  yielding  to  the  touch, 
steaming,  &c.,  all  of  which  properties  it  again  loses 
on  the  departure  of  the  heat.  If  taken  from  the  cru- 
cible and  thrown  upon  paper,  it  will  not  wet  it,  but 
immediately  be  as  motionless  as  it  was  before  being 
exposed  to  the  heat. 

Two  or  three  spoonfuls  of  burnt  alabaster  mixed 
up  thin  with  water  will,  at  the  bottom  of  a  vessel 
filled  with  water,  coagulate  into  a  hard  lump,  not- 


withstanding the  water  that  surrounds  it. 


The  coag- 


ulating or  setting  property  of  burnt  alabaster  will  be 
very  much  impaired  or  lost  if  the  powder  be  kept  for 
any  considerable  time,  and  more  especially  in  the 
open  au-.  When  it  has  been  once  tempered  with 
water,  and  suffered  to  grow  hard,  it  cannot  be  ren- 
dered of  any  further  use. 

Plaster  of  Paris,  diluted  with  water  into  the  con- 
sistence of  a  soft  or  thin  paste,  quickly  sets,  or  grows 
firm,  and,  at  the  instant  of  its  setting,  has  its  bulk 
increased.  This  expansive  property,  in  passing  from 
a  soft  to  a  firm  state,  is  one  of  its  valuable  properties, 
rendering  it  an  excellent  matter  for  filling  cavities  in 
sundry  works,  where  other  earthy  mixtures  would 
shrink  and  leave  vacuities,  or  entirely  separate  from 
the  adjoining  parts.  It  is  also  probable  that  this  ex- 
pansion of  the  plaster  might  be  made  to  contribute 
to  the  elegance  of  the  impressions  it  receives  from 
medals,  &c.,  by  properly  confining  it  when  soft,  so 
that,  at  its  expansion,  it  would  be  forced  into  the  mi- 
nutest traces  of  the  figures. 

Other  cements  are  iised  by  plasterers  for  inside 
work.  The  first  is  called  lime  and  hair,  or  coarse 
stuff,  and  is  prepared  as  common  mortar,  with  the 
addition  of  hair  from  the  tan  yards.  The  mortar  is 
first  mixed  with  a  requisite  quantity  of  sand,  and  the 
hair  is  afterwards  worked  in  by  the  appKcation  of  a 
rake. 

Next  to  this  is  fine  stuff,  which  is  merely  pure  lime, 
slaked  first  with  a  small  quantity  of  water,  and 
afterwards,  without  any  extraneous  addition,  super- 
saturated with  water,  and  put  into  a  tub  in  a  half 
fluid  state,  where  it  is  allowed  to  remain  till  the  water 
is  evaporated.  In  some  particular  cases,  a  small  por- 
tion of  hair  is  incorporated.  When  this  fine  stuff 
is  used  for  inside  walls,  it  is  mixed  with  very  fine 
washed  sand,  in  the  proportion  of  one  part  sand  to 
three  parts  of  fine  stuff,  and  is  then  caUed  trowelled 


or  bastard  stucco,  with  which  all  walls  intended  to  be 
painted  are  finished. 

The  cement  called  ^augc  stuff  consists  of  three 
fifths  of  fine  stuff"  and  one  fifth  plaster  of  Paris,  mixed 
together  with  water,  in  small  quantities  at  a  time,  to 
render  it  more  ready  to  set.  This  composition  is 
mostly  used  in  forming  cornices  and  mouldings  run 
with  a  wooden  mould.  When  great  expedition  is 
required,  plasterers  gauge  all  their  mortars  with  plas- 
ter of  Paris,  which  sets  immediately. 


MASTIC    CEMENT. 

This  useful  invention  consists  in  making  a  cement 
or  composition,  which  may  be  applied  in  the  for- 
mation of  ornaments  and  statues,  and  of  bricks,  or 
an  imitation  of  bricks,  tiles,  and  stones,  and  joining 
and  cementing  the  same,  and  in  erecting,  covering, 
and  decorating  buildings  internally  and  externally ; 
and  the  said  cement  or  composition  may  be  mixed 
and  moulded  upon  any  sort  of  material,  and  whole 
and  entire  erections  and  substances  may  be  worked 
and  moulded  therewith. 

The  cement  consists  in  a  mixture  of  earths  and 
other  substances  that  are  insoluble  in  water,  or  nearly 
so,  either  in  their  natural  state,  or  such  as  have  been 
manufactured,  as  earthen  ware,  porcelain,  and  such 
like  substances ;  but  it  is  preferred  that  those  earths, 
either  in  their  natural  or  manufactmred  state,  are  the 
least  soluble  in  water,  and  have,  when  pulverized,  or 
reduced  to  powder,  the  least  color.  To  the  earth  or 
earths  as  before  named,  either  in  their  natural  or  man- 
ufactured state,  and  so  pulverized,  add  a  quantity  of 
each  of  the  oxides  of  lead,  as  litharge,  gray  oxide,  and 
minium,  reduced  or  ground  to  powder,  and  to  the 
whole  of  the  above-named  substances  a  quantity  of 
pulverized  glass  or  flint  stone 

These  various  earths,  oxides,  and  glass,  or  flijit  stone, 
reduced  to  a  pulverized  state,  in  proper  and  due  pro- 
portions, and  being  mixed  with  a  proper  and  due 
proportion  of  vegetable  oil,  as  hereinafter  named, 
form  and  make  a  composition  or  cement,  which,  by 
contact  or  exposure  to  the  atmosphere,  hardens  and 
forms  an  impenetrable  and  impervious  coating  or 
covering,  resembling  Portland  or  other  stones. 

The  cement  or  composition  is  composed  in  the 
following  manner  and  proportions :    To  any  given 


152 


BUILDING. 


weight  of  earth  or  earths,  commonly  called  pit  sand, 
river  sand,  rock  sand,  or  any  other  sand  of  the  same 
or  like  nature,  or  pulverized  earthen  ware,  or  porce- 
lain, add  two  thirds  of  such  given  weight  of  the  earth 
or  earths  commonly  called  Portland  stone,  Bath 
stone,  or  any  other  stone  of  the  same  or  like  nature, 
pulverized.  To  every  five  hundred  and  sixty  pounds' 
weight  of  these  earths  so  prepared  add  forty  pounds' 
weight  of  litharge,  prepared  as  before  described,  and, 
with  the  last-mentioned  given  weights,  combine  two 
pounds'  weight  of  pulverized  glass  or  flint  stone. 

Then  join  to  this  mixture  one  pound  weight  of  min- 
ium and  two  pounds'  weight  of  gray  oxide  of  lead. 

This  compound  of  earths,  oxide,  and  glass,  or  flint 
stone,  put  into  a  circular  or  other  proper  machine, 
that  will,  by  its  rotary  or  other  motion,  mix  them  well, 
and  their  proper  intermixture  may  be  ascertained  by 
the  shade  or  colors,  which  should  appear  of  one  even 
and  regular  shade  or  hue  ;  but  any  particular  shade 
or  color  may  be  given  by  a  proper  selection  of  earths, 
or  by  adding  a  small  quantity  of  vegetable,  mineral, 
or  other  coloring  matter. 

This  composition  being  thus  mixed,  pass  the  same 
through  a  wire  sieve,  or  dressing  machine,  of  such 
fineness  or  mash  as  may  be  requisite  for  the  purposes 
it  is  intended  for,  preferring  a  fine  sieve,  mash  or  wire 
work,  when  the  composition  is  to  be  used  for  works 
of  a  fine  or  even  surface.  The  composition  thus 
formed  and  mixed  is  a  fine  dry  powder,  and  may  be 
kept  open  in  bulk  or  in  casks  for  any  length  of  time 
without  deterioration. 

When  this  composition  is  intended  to  be  made 
into  cement  for  any  of  the  purposes  described,  it  is 
spread  upon  a  board  or  platform,  or  mixed  in  a  trough ; 
and  to  every  six  hundred  and  five  pounds'  weight  of 
the  composition  are  added  five  gallons  of  vegetable 
oil,  as  linseed  oil,  v^^alnut  oil,  or  pink  oU. 

The  composition  is  then  mixed  in  a  similar  way 
to  that  of  the  mortar,  and  is  afterwards  subjected  to 
a  gentle  pressure  by  treading  upon  it ;  and  this  oper- 
ation is  continued  until  it  acquires  the  appearance 
of  moistened  sand.  The  mixture  being  thus  com- 
posed is  a  cement  fit  and  applicable  to  the  enume- 
rated purposes.  It  is  requisite  to  observe,  that  this 
cement  should  be  used  the  same  day  the  oil  is  added, 
otherwise  it  wiU  fix  or  set  into  a  solid  substance,  and 
be  unfit  for  use. 

When  this  cement  is  to  be  used  or  applied  to  any 
thing,  —  to  making  of  decorations,  ornaments,  and 


statues,  or  artificial  bricks,  tiles,  and  stones,  —  running 
or  casting  moulds,  prepared,  suited,  and  applicable 
for  the  purposes  for  which  they  are  intended,  are  made 
use  of.  The  moulds  for  making  ornaments,  statues, 
or  other  fancy  works  are  prepared  and  made  of  gyp- 
sum, or  plaster  of  Paris,  or  seasoned  or  dry  wood, 
and  must  be  prepared  by  rubbing  the  internal  parts 
well  with  raw  linseed  oil,  until  they  are  brought  to  a 
dry,  smooth,  and  polished  surface,  to  prevent  adhe- 
sion ;  and  in  some  instances,  to  obtain  a  more  per- 
fect, dry,  smooth,  and  polished  surface,  pulverized 
plumbago  is  used.  In  all  cases  it  is  requisite  to  de- 
tach or  remove,  with  convenient  speed,  the  mould 
from  the  body  of  the  cement  or  composition  to  which 
it  is  intended  to  give  form. 

The  statue,  ornament,  bricks,  tiles,  and  stones,  or 
the  imitations  of  all  or  either  of  them,  thus  formed, 
must  be  removed  with  care,  and  placed  upon  a  bench 
or  platform,  which  must  be  previously  covered  with 
fine  dry  sand  to  prevent  adhesion ;  and,  in  some 
cases,  for  statues  and  ornaments,  a  bed  of  fine  dry 
sand  is  necessary  to  receive  them,  where  they  must 
remain  in  both  cases  for  the  purpose  of  setting  for 
twenty-four  hours,  or  a  longer  period,  according  to 
the  temperature  to  which  they  are  exposed. 

When  it  is  applied  for  the  purpose  of  cementing 
and  joining  of  bricks,  tiles,  stones,  and  other  sub- 
stances, the  surfaces  to  which  the  cement  or  compo- 
sition is  to  be  applied  are  prepared  by  brushing  and 
cleaning  them  from  dust  and  all  loose  matter ;  the 
said  surfaces  are  then  covered  with  boiled  linseed 
oil,  with  a  brush,  as  in  painting.  This  application 
of  the  boiled  linseed  oil  prevents  the  too  rapid  ab- 
sorption of  the  oil  employed  or  mixed  with  the  cem- 
ent or  composition.  A  thin  coating  of  the  cement  is 
then  applied  between  the  two  bodies  to  be  joined. 
When  the  cement  is  used  for  the  purpose  of  covering 
buildings  intended  to  resemble  stone,  the  surface  of 
the  buildings  is  washed  in  oil. 

The  cement  is  then  applied  of  the  thickness  of  a 
quarter  of  an  inch,  or  any  greater  thickness,  accord- 
ing to  the  nature  of  the  work,  joint,  or  stone  it  is 
intended  to  resemble. 

It  is  requisite  to  observe,  that  when  a  joint,  in- 
tended to  resemble  a  plain  stone  joint,  is  to  be  made 
upon  the  surface  of  the  cement  or  composition,  the 
cement  or  composition  must  be  partly  set  or  hardened 
previously  to  the  impression  of  the  joint  upon  its  sur- 
face, and  the  joint  is  made  by  a  rule  and  steel  jointer. 


BUILDING. 


153 


When  the  cement  is  used  for  the  covering  of  sub- 
stances less  absorbent  than  briclcs,  or  tiles,  (as  wood, 
lead,  iron,  or  tin,)  a  much  less  quantity  of  boiled 
linseed  oil  in  preparing  the  surfaces  is  required. 


LATHING,    PLASTERING,    &c. 

Lathinff,  the  fii-st  operation,  consists  in  nailing 
laths  on  the  ceiling  or  partition.  Laths  are  made  of 
spruce  or  pine,  and  are  fastened  with  cut  nails.  They 
are  made  in  fom'-foot  lengths  ;  and,  with  respect  to 
their  thiclaaess  and  strength,  are  either  smgle,  lath 
and  half,  or  double.  The  single  are  the  thinnest  and 
cheapest ;  those  called  lath  and  half  are  supposed  to 
be  one  third  thicker  than  the  smgle ;  and  the  double 
laths  are  twice  that  thickness.  In  lathing  ceilings, 
the  plasterers  should  so  dispose  them  that  the  joints 
be  as  much  broken  as  possible,  that  they  may  have 
the  stronger  key  or  tie,  and  thereby  strengthen  the 
plastering  with  which  they  are  to  be  covered.  The 
thinnest  laths  are  used  in  partitions,  and  the  strongest 
for  ceilings. 

Latlis  are  also  distinguished  into  heart  and  sap 
laths :  the  former  should  always  be  used  in  plain 
tiling ;  the  latter,  which  are  of  inferior  quality,  are 
most  frequently  used  by  the   plasterer. 

Sawed  laths  have  within  a  few  years  been  inti-o- 
duced,  and  are  nov/  in  general  use.  They  are  not 
subject  to  so  much  waste,  cost  less,  and  do  not  re- 
quire so  much  mortar  as  the  split  lath;  the  last 
named,  however,  retains  the  mortar  most  firmly. 

Having  nailed  the  laths  in  then-  appropriate  order, 
the  plasterer's  next  business  is  to  cover  them  with 
plaster,  the  most  sim.ple  and  common  operation  of 
which  is  laying ;  that  is,  spreading  a  single  coat  of 
lime  and  hair  over  the  whole  ceiling  or  partition, 
carefully  observing  to  keep  it  smooth  and  even  in 
every  direction.  This  is  the  cheapest  kind  of  plas- 
tering. 

Pricking  up  is  performed  in  the  same  manner  as 
the  foregoing ;  but  it  is  only  a  preliminary  to  a  more 
perfect  Idnd  of  work.  After  the  plaster  is  laid  on,  it 
is  crossed  all  over  V;dth  the  end  of  a  lath,  to  give  it  a 
tie  or  key  to  the  coat  which  is  afterwards  to  be  laid 
upon  it. 

Lathing,  laying,  and  set,  or  what  is  termed  lath  and 
plaster,  one  coat  and  set,  is,  when  the  work,  after 

20 


being  lathed,  is  covered  with  one  coat  of  lime  and 
hair,  and  aftei-^ards,  when  sufficiently  dry,  a  thin  and 
smooth  coat  is  spread  over  it,  consisting  of  lime  only, 
or,  as  the  workmen  call  it,  putty  or  set.  This  coat  is 
spread  with  a  smoothing  trowel,  used  by  the  work- 
man with  his  right  hand,  while  his  left  hand  moves 
a  large  flat  brush  of  hogs'  bristles,  dipped  in  water, 
backwards  and  forwards  over  it,  and  thus  produces  a 
sm-facc  tolerably  even  for  cheap  work. 

Lathing,  floating  and  set,  or  lath  and  plaster,  one 
coat,  floated  and  set,  differs  from  the  foregoing,  in 
having  the  first  coat  pricked  up  to  receive  the  set, 
which  is  here  called  the  floating.  In  doing  this,  the 
plasterer  is  provided  with  a  substantial  straight  edge, 
frequently  from  ten  to  twelve  feet  in  length,  which 
must  be  used  by  two  workmen.  All  the  parts  to 
be  floated  arc  tried  by  a  straight  edge,  to  ascertain 
whether  they  be  perfectly  flat  and  level ;  and  whenever 
any  deficiency  appears,  the  hollow  is  filled  up  with  a 
trowel  full  or  more  of  lime  and  hair  only,  which  is 
termed  fllling  out ;  and  when  these  preliminaries  are 
settled,  the  screeds  are  next  formed.  The  term  screed 
signifies  a  style  of  Hme  and  hair,  about  seven  or 
eight  inches  in  width,  gauged  quite  true,  by  drawing 
the  straight  edge  over  it  until  it  be  so.  These  screeds 
are  made  at  the  distance  of  about  three  or  four  feet 
from  each  other,  in  a  vertical  dh-cction,  all  round 
the  partitions  and  walls  of  a  room.  When  all  are 
formed,  the  intervals  are  filled  up  with  lime  and  hair, 
called  by  the  workmen  stuff,  till  flush  with  the  face 
of  the  screeds.  The  straight  edge  is  then  worked 
horizontally  on  the  screeds,  by  which  aU  the  super- 
fluous stuff  projecting  beyond  them  in  the  intervals 
is  removed,  and  a  plain  sm-face  produced.  This 
operation  is  termed  floating,  and  may  be  applied  to 
ceilings  as  well  as  to  partitions  or  upright  walls,  by 
first  forming  the  screeds  in  the  dkcction  of  the 
breadth  of  the  apartment,  and  filling  up  the  intervals 
as  above  described.  As  great  care  is  requisite  to 
render  the  plaster  sound  and  even,  none  but  skilful 
workmen  should  be  employed. 

The  set  to  floated  work  is  performed  in  a  mode 
similar  to  that  aheady  prescribed  for  laying;  but, 
being  employed  only  for  best  rooms,  is  done  with 
more  care.  About  one  sLxth  of  plaster  of  Paris  is 
added  to  it,  to  make  it  set  more  expeditioiisly,  to 
give  it  a  closer  and  more  compact  appearance,  and 
to  render  it  more  firm,  and  better  calcidated  to  re- 
ceive the  whitewash  or  color  when  dry.     For  floated 


154 


BUILDING. 


stucco  work,  the  pricking  up  cannot  be  too  dry ;  but 
if  the  floating  which  is  to  receive  the  setting  coat 
be  too  dry  before  the  set  is  laid  on,  there  will  be 
danger  of  its  peeling  off,  or  of  assuming  the  appear- 
ance of  little  cracks  or  sliclls,  which  would  disfigiu-e 
the  work.  Particular  care  and  attention,  therefore, 
must  be  paid  to  have  the  under  coats  in  a  proper 
state  of  dryness.  It  may  here  be  observed,  that 
cracks,  and  other  unpleasant  appearances  in  ceilings, 
are  more  frequently  the  effect  of  weak  laths  being 
covered  with  too  much  plaster,  or  too  little  plaster 
upon  strong  laths,  rather  than  of  any  sagging  or 
other  inadequacy  in  the  timbers  or  the  building.  If 
the  laths  be  properly  attended  to,  and  the  plaster  laid 
on  by  a  careful  and  judicious  workman,  no  cracks  or 
other  blemishes  are  likely  to  appear. 

The  next  operation  combines  both  the  foregoing 
processes,  but  requires  no  lathing ;  it  is  called  render- 
ing-  and  set,  or  rendering,  floated,  and  set.  What  is 
understood  by  rendering,  is  the  covering  of  brick  or 
stone  wall  with  a  coat  of  lime  and  hair,  and  by  set  is 
denoted  a  superficial  coat  of  fine  stuff  or  putty  upon 
the  rendering.  These  operations  are  similar  to  those 
described  for  setting  of  ceilings  and  partitions ;  and 
the  floated  and  set  is  laid  on  the  rendering  in  the 
same  manner  as  on  the  partitions,  &c.,  akeady  ex- 
plained, for  the  best  kind  of  work. 

Trowelled  stucco,  which  is  a  very  neat  kind  of 
work,  used  in  dining-rooms,  halls,  &c.,  where  the 
walls  are  prepared  to  be  painted,  must  be  worked 
upon  a  floated  ground,  and  the  floating  be  kept  quite 
dry  before  the  stucco  is  applied.  In  this  process,  the 
plasterer  is  provided  with  a  wooden  tool,  called  a 
Hoat,  consisting  of  a  piece  of  half-inch  board,  about 
nine  inches  long  and  three  wide,  planed  smooth, 
with  its  lower  edges  a  little  rounded  off,  and  having 
a  handle  on  the  upper  surface.  The  stucco  is  pre- 
pared as  above  described,  and  afterwards  beaten  and 
tempered  with  clear  water.  The  ground  intended  to 
be  stuccoed  is  first  prepared  with  a  large  trowel,  and 
is  made  as  smooth  and  level  as  possible ;  when  the 
stucco  has  been  spread  upon  it  to  the  extent  of  four 
or  five  feet  square,  the  workman,  with  a  float  in  his 
right  hand  and  a  brush  in  his  left,  sprinkles  with 
water  and  rubs  alternately  the  face  of  the  stucco,  till 
the  whole  is  reduced  to  a  fine,  even  surface.  He 
then  prepares  another  square  of  the  ground,  and  pro- 
ceeds as  before,  till  the  whole  is  completed.  The 
water  lias  the  effect  of  hardening  the  face  of  the 


stucco.  When  the  floating  is  well  performed,  it  will 
feel  as  smooth  as  glass. 

Rovgh  casting,  or  rough  tvalling,  is  an  exterior  fin- 
ishing, much  cheaper  than  stucco,  and,  therefore,  more 
frequently  employed  on  cottages,  farm-houses,  &c., 
than  on  buildings  of  a  higher  class.  The  wall  in- 
tended to  be  rough  cast  is  first  picked  up  with  a  coat  of 
lime  and  hair ;  and  when  this  is  tolerably  dry,  a  sec- 
ond coat  is  laid  on,  of  the  same  materials  as  the  first, 
as  smooth  as  it  can  possibly  be  spread.  As  fast  as 
the  workman  finishes  this  surface,  he  is  followed  by 
another  'with  a  pailful  of  rough  cast,  with  v\'^hich  he 
bespatters  the  new  plastering,  and  the  whole  dries 
together.  The  rough  cast  is  composed  of  fine  gravel, 
washed  from  all  earthy  particles,  and  mixed  with 
pure  lime  and  water,  till  the  whole  is  of  a  semi-fluid 
consistency.  This  is  thrown  from  the  pad  upon  the 
wall  with  a  wooden  float,  about  five  or  six  inches 
long,  and  as  many  wide,  made  of  half-inch  board, 
and  fitted  with  a  round  handle.  While,  with  tliis 
tool,  the  plasterer  throws  en  the  rough  cast  with  his 
right  hand,  he  holds  in  his  left  a  common  wliite- 
washer's  brush,  dipped  in  the  rough  cast  also,  with 
which  he  brushes  and  colors  the  mortar  and  the 
rough  cast  he  has  already  spread,  to  give  them,  when 
finished,  a  regular,  uniform  color  and  appearance. 

Cornices  are  either  plain  or  ornamented,  and  some- 
times embrace  a  portion  of  both  classes.  The  first 
point  to  be  attended  to  is,  to  examine  the  drawings, 
and  measure  the  projections  of  the  principal  mem- 
bers, which,  if  projecting  more  than  seven  or  eight 
inches,  must  be  bracketed.  This  consists  in  fixing 
up  pieces  of  wood  at  the  distance  of  about  ten  or 
twelve  inches  from  each  other,  all  round  the  place 
proposed  for  the  cornice,  and  nailing  laths  to  them, 
covering  the  whole  with  a  coat  of  plaster.  In  the 
brackets,  the  stuff  necessary  to  form  the  cornice  must 
be  allowed,  which,  in  general,  is  about  one  inch  and 
a  quarter.  A  beech  mould  is  next  made  by  the  car- 
penter, of  the  profile  of  the  intended  cornice,  about 
a  quarter  of  an  inch  iii  thickness,  with  the  quirks,  or 
small  sinkings,  of  brass  or  copper.  All  the  sharp 
edges  are  carefully  removed  by  the  plasterer,  who 
opens  with  his  knife  all  the  points  v/hich  he  finds 
incompetent  to  receive  the  plaster  freely. 

These  preliminaries  being  adjusted,  two  workmen, 
provided  vdth  a  tub  of  putty  and  a  quantity  of  plas- 
ter of  Paris,  proceed  to  run  the  cornice.  Before 
using  the  mould,  they  gauge    screed  of  putty  and 


BUILDING. 


155 


plaster  upon  the  wall  and  ceiling,  covering  so  much 
of  each  as  will  correspond  with  the  top  and  bottom 
of  the  intended  cornice.  On  this  screed,  one  or  two 
slight  board  straight  edges,  adapted  to  as  many 
notches  or  chases,  made  in  the  mould  for  it  to  work 
upon,  are  naUed.  The  putty  is  then  mixed  with 
about  one  third  of  plaster  of  Paris,  and  brought  to 
a  semi-fluid  state  by  the  addition  of  clean  water. 
One  of  the  workmen,  with  two  or  three  ti'owels  full 
of  this  composition  upon  his  liau'k,  which  he  holds 
in  his  left  hand,  begins  to  plaster  over  the  surface 
intended  for  the  cornice,  wuth  his  trowel,  while  his 
partner  applies  the  mould  to  ascertain  when  more  or 
less  is  wanted.  When  a  sufficient  quantity  of  plas- 
ter is  laid  on,  the  workman  holds  his  mould  firmly 
against  both  the  ceiling  and  the  wall,  and  moves  it 
backwards  and  forwards,  which  removes  the  super- 
fluous stuff,  and  leaves  an  exact  impression  of  the 
mould  upon  the  plaster.  This  is  not  effected  at 
once  ;  for  while  he  works  the  mould  backwards  and 
forwards,  the  otlicr  workman  takes  notice  of  any  de- 
ficiencies, and  fills  them  up  by  adding  fi-esh  supplies 
of  plaster.  In  this  manner,  a  cornice  from  ten  to 
ttt^elve  feet  in  length  may  be  formed  in  a  very  short 
time;  indeed,  expedition  is  essentially  requisite,  as 
the  plaster  of  Paris  occasions  a  very  great  tendency 
in  the  putty  to  set ;  to  prevent  which,  it  is  necessary 
to  sprinkle  the  composition  frequently  with  water,  as 
plasterers,  in  order  to  secure  the  truth  and  coiTectness 
of  the  cornice,  generally  endeavor  to  finish  aU  the 
lengths  or  pieces  between  any  two  breaks  or  pro- 
jections at  one  time.  In  cornices  which  have  very 
large  proportions,  and  in  cases  where  any  of  the  or- 
ders of  arcliiteeture  are  to  be  introduced,  three  or 
four  moulds  are  required,  and  are  sim.ilarly  applied, 
till  all  the  parts  are  formed.  Litcrnal  and  external 
mitres,  and  small  returns  or  breaks,  are  afterwards 
modelled  and  filled  up    by  hand. 

Cornices  to  be  enriched  with  ornaments  have  cer- 
tam  indentations,  or  sinldngs,  left  in  the  mould  in 
which  the  casts  are  laid.  These  ornaments  were 
formerly  made  by  hand,  but  now  are  cast  in  plaster 
of  Paris,  from  clay  models.  When  the  clay  model 
is  finished,  and  has,  by  exposure  to  the  action  of  the 
atmosphere,  acquired  some  degree  of  firmness,  it  is 
let  into  a  wooden  firame,  and,  when  it  has  been  re- 
touched and  finished,  the  frame  is  fiUed  with  melted 
wax,  which,  when  cold,  is,  by  turning  the  frame  up- 
side down,  allowed  to  fall  ofl',  being  an  exact  cameo. 


or  counterpart  of  the  model.  By  these  means,  the 
most  enriched  and  curiously-wrought  mouldings  may 
be  cast  by  the  common  plasterer.  These  wax  mod- 
els are  contrived  to  east  about  a  foot  in  length  of  the 
ornament  at  once,  such  lengths  being  easily  got  out 
from  the  cameo.  The  casts  are  made  of  the  finest 
and  purest  plaster  of  Paris,  saturated  with  water; 
and  the  wax  mould  is  oiled  previously  to  its  being 
put  in.  When  the  casts  or  intaglios  arc  first  taken 
from  tlie  mould,  they  are  not  very  firm ;  but  being 
suffered  to  dry  a  little,  either  in  the  open  air  or  in  an 
oven,  they  acquke  sufficient  hardness  to  allow  of 
being  scraped  and  cleaned. 

Basso  rUievos  and  friezes  are  executed  in  a  similar 
manner,  only  the  wax  mould  is  so  made  that  the 
cast  can  have  a  back  ground  at  least  half  an  inch 
thick  of  plaster  cast  to  the  ornament  or  figure,  in 
order  to  strengthen  and  secure  the  proportions,  at  the 
same  time  that  it  promotes  the  general  effect. 

The  process  for  capitals  to  columns  is  also  the 
same,  except  that  numerous  moulds  arc  required  to 
complete  them.  In  tlic  Corinthian  capitals,  a  shaft 
or  belt  is  first  made,  on  which  is  afterwards  fixed  the 
foliage  and  volutes,  the  whole  of  which  require  dis- 
tinct cameos. 

In  running  cornices,  which  arc  to  be  enriched,  the 
plasterer  takes  care  to  have  proper  projections  in  the 
running  moulds,  so  as  to  make  a  groove  in  the  cor- 
nice for  the  reception  of  the  cast  ornament,  v/hich  is 
laid  in  and  secured  by  spreading  a  siuall  quantity  of 
liquid  plaster  of  Paris  on  its  back.  Detached  orna- 
ments intended  for  ceilings  or  other  parts,  and  where 
no  running  mould  has  been  employed,  are  cast  in 
pieces  corresponding  with  the  design,  and  fixed  upon 
the  ceiling,  &c.,  with  white  lead,  or  with  the  compo- 
sition known  by  the  name  of  iron  cement. 

The  manufacture  of  stucco  has,  for  a  long  time 
past,  attracted  the  attention  of  all  connected  with 
this  branch  of  building,  as  well  as  chemists  and  other 
individuals ;  but  the  only  benefit  resulting  from  such 
investigations  is,  a  more  extensive -knowledge  of  the 
materials  used.  It  would  seem  that  the  gi-eat  moist- 
m-e  of  our  climate  prevents  its  being  brought  to  any 
high  degree  of  perfection  ;  though,  among  the  various 
compositions  which  have  been  tried  and  proposed, 
some,  .comparatively  speaking,   are  excellent. 

Common  stucco,  used  for  external  work,  consists 
of  clean-washed  river  sand  and  ground  lime,  which  are 
mixed  dry,  in  the  proportion  of  three  of  the  latter  to 


156 


BUILDING. 


one  of  the  former :  when  well  incorporated  together, 
these  should  be  secured  from  the  air  in  casks  till  re- 
quired for  use.  Walls  to  be  covered  with  this  com- 
position must  first  be  prepared,  by  raking  the  mortar 
from  the  joints,  and  picking  the  bricks  or  stones,  till 
the  whole  is  indented  ;  the  dust  and  other  extraneous 
matter  must  then  be  brushed  off,  and  the  wall  well 
saturated  with  clean  water.  The  stucco  is  supersat- 
luatcd  with  water  till  it  has  the  appearance  and  con- 
sistence of  ordinary  whitewash,  in  which  state  it  is 
rubbed  over  the  wall  with  a  flat  brush  of  hogs'  bris- 
tles. When  this  process,  called  roughing  in,  has  been 
performed,  and  the  work  has  become  tolerably  chy 
and  hard,  which  may  be  known  by  its  being  more 
white  and  transparent,  the  screeds  are  to  be  formed 
upon  the  wall  with  fresh  stucco  from  the  cask,  tem- 
pered with  water  to  a  proper  consistency,  and  spread 
on  the  upper  part  of  the  wall,  about  eight  or  nine 
inches  wide ;  as  also  against  the  two  ends,  beginning 
at  the  top,  and  proceeding  downwards  to  the  bottom. 
Li  this  operation,  two  workmen  arc  required ;  one  to 
supply  the  stucco,  the  other  to  apply  the  plumb  ride 
and  sh-aight  edge.  When  these  are  truly  formed, 
other  screeds  must  be  made  in  a  vertical  direction, 
about  fom"  or  five  feet  apart,  unless  apertures  in  the 
wall  prevent  it ;  in  which  case,  they  must  be  formed 
as  near  together  as  possible.  When  the  screcding  is 
finished,  compo  *  is  prepared  in  larger  quantities,  and 
both  the  workmen  spread  it  with  their  trowels  over 
the  wall,  in  the  space  left  between  each  pair  of 
screeds.  When  this  operation  is  complete,  the 
straight  edge  is  applied,  and  dragged  from  the  top  to 
the  bottom  of  each  pair,  to  remove  whatever  super- 
fluous stucco  may  project  above  the  screeds.  If 
there  be  any  hollow  places,  fresh  stucco  is  applied, 
and  the  straight  edge  is  again  drawn  over  the  spot, 
till  the  compo  is  brought  even  to  the  face  of  the 
screeds,  and  the  whole  is  level  with  the  edge  of  the 
rule.  Another  interval  is  then  filled  xip,  and  the 
workmen  thus  proceed  till  the  whole  of  the  wall  is 
covered.  The  wall  is  finished  by  floating;  that  is, 
hardening  the  surface  by  sprinkling  it  with  water, 
and  rubbing  it  with  the  common  wood  float,  which 
is  performed  similarly  to  trowelling  stucco. 

This  description  of  compo  is  frequently  used  by 
plasterers  for  cornices  and  mouldings,  in  the  same 
manner  as  described  in  common  plastering;  but  if 

*  A  name  often  given  to  Parker'i?  cement. 


the  workman  finds  it  necessary,  he  may  add  a  small 
quantity  of  plaster  of  Paris,  to  make  it  fix  the  better 
while  running  or  working  the  mould.  Such  addition 
is  not,  however,  calculated  to  give  strength  to  the 
stucco,  and  is  only  made  through  the  necessity  of 
having  a  quick  set. 

Scag-Uola  is  a  distinct  branch  of  plastering,  dis- 
covered or  invented,  and  much  used,  in  Italy,  and 
thence  introduced  into  France,  where  it  obtained  its 
name. 

Columns  and  pilasters  are  executed  in  this  branch 
of  plastering  in  the  following  manner:  A  wooden 
cradle,  composed  of  thin  strips  of  pine  or  other  wood, 
is  naade  to  represent  the  column  designed,  but  about 
two  inches  and  a  half  less  in  diameter  than  the  shaft 
is  intended  to  be  when  finished.  This  cradle  is  lathed 
round,  as  for  common  plastering,  and  then  covered 
with  a  pricking-up  coat  of  lime  and  hair.  Wlien 
this  is  quite  dry,  the  artists  in  scagliola  commence 
operations,  by  imitations  of  the  most  rare  and  pre- 
cious marbles,  with  astonishing  and  delusive  effect ; 
indeed,  as  the  imitation  takes  as  high  a  polish,  and 
feels  as  cold  and  hard,  as  the  most  compact  and  solid 
marble,  nothing  short  of  actual  fracture  can  possibly 
discover  the  counterfeit. 

In  preparing  the  scagliola,  the  workman  selects, 
breaks,  and  calcines  the  purest  gypsum,  and  as  soon 
as  the  largest  fragments,  in  the  process  of  calcination, 
lose  their  brilliancy,  withch-aws  the  fire,  and  passes 
the  calcined  powder  through  a  very  fine  sieve,  and 
mixes  it,  as  required  for  use,  with  a  solution  of  glue, 
isinglass,  &c.  In  this  solution,  the  colors  required  in 
the  marble  to  be  imitated  arc  diffused  ;  but  when  the 
work  is  to  be  of  various  colors,  each  color  is  prepared 
separately,  and  afterwards  mmgled  and  combined, 
nearly  in  the  same  manner  as  a  painter  mixes  oia  his 
palette  the  primitive  colors  to  compose  his  different 
tints. 

When  the  powdered  gypsum  is  prepared,  it  is  laid 
on  the  shaft  of  the  intended  column,  over  the  pricked- 
up  coat  of  lime  and  hair,  and  is  then  floated  with 
moulds  of  wood,  made  to  the  requisite  size  :  the  artist 
iises  the  colors  necessary  to  the  imitation  dm'ing  the 
floating,  by  which  means  they  mingle  and  incorpo- 
rate with  the  surface.  To  obtain  the  glossy  lustre, 
so  much  admired  in  works  of  marble,  the  workman 
rubs  the  work  with  one  hand  with  a  pumice  stone, 
while  with  the  other  he  cleans  it  with  a  wet  sponge ; 
he  next  polishes  it  with  tripoli,  charcoal,  and  a  piece 


BUILDING. 


157 


of  fine  linen ;  aftenvards  with  a  piece  of  felt,  dipped 
in  a  mixtnre  of  oil  and  tripoli ;  and  finally  completes 
the  work  by  the  application  of  piu-e  oil.  This  imita- 
tion is,  certainly,  the  most  complete  that  can  be  con- 
ceived ;  and  wlion  the  bases  and  capitals  arc  made 
of  real  marble,  as  is  the  common  practice,  the  de- 
ception is  beyond  discovery.  K  not  exposed  to  the 
weather,  it  is,  in  point  of  durability,  little  inferior  to 
real  marble,  retains  its  lustre  full  as  long,  and  is  not 
one  eighth  of  the  expense  of  the  cheapest  kind. 

There  is  another  species  of  plastering,  used  in  the 
decorative  parts  of  architecture,  and  for  the  frames 
of  pictures,  looking-glasses,  &c.,  which  is  a  perfectly 
distinct  branch  of  the  art.  This  composition,  which 
is  very  strong,  and,  when  quite  dry,  of  a  brownish 
color,  consists  of  the  proportion  of  two  pounds  of 
powdered  whiting,  one  pound  of  glue  in  solution, 
and  half  a  pound  of  linseed  oil,  mixed  together,  and 
heated  in  a  copper,  and  stin-ed  with  a  spatula  till  the 
whole  is  incorporated.  When  cool,  it  is  laid  upon  a 
stone,  covered  with  powdered  whiting,  and  beaten  till 
it  assumes  a  tough  and  firm  consistence  ;  after  which 
it  is  covered  with  wet  cloths,  to  keep  it  fresh  till  re- 
quu-ed  for  use. 

The  ornaments  to  be  cast  in  this  composition  are 
modelled  in  clay,  as  in  common  plastering,  and  af- 
terwards a  cameo,  or  mould,  is  carved  in  boxwood. 
This  carving  requires  to  be  done  with  the  utmost 
care,  otherwise  the  symmetry  of  the  ornament  which 
is  to  be  cast  from  it  will  be  sjjoUed.  The  composi- 
tion, when  required  for  use,  is  cut  with  a  knife  into 
pieces  of  the  requisite  size  and  forced  into  the  mould  ; 
after  which  it  is  put  into  a  press  worked  by  an  iron 
screw,  and  still  further  compressed.  When  the  mould 
is  taken  from  the  press,  the  composition,  which  is 
generally  cast  about  a  foot  in  length,  is  dislodged 
from  the  mould,  and  the  superfluous  parts  pared 
off  with  a  knife  and  cast  into  the  copper  for  the 
next    supply. 

The  ornaments  thus  formed  are  glued  upon  wooden 
grounds,  or  fixed  by  means  of  white  lead,  &c. ;  after 
which  they  are  painted  or  gUt,  according  to  the  pur- 
poses for  which  they  are  intended.  This  composition 
is  at  least  80  per  cent,  cheaper  than  carving,  and,  in 
most  cases,  equally  calculated  to  answer  all  the  pur- 
poses of  the  art. 

It  is  much  to  be  wished,  that  the  art  of  plastering 
could  be  restored  to  its  ancient  perfection,  for  the 
Romans  possessed  an  art  of  rendering  works  of  this 


kind  much  more  firm  and  durable  than  can  be  ac- 
complished at  the  present  time. 

The  specimens  of  ancient  Roman  plastering  still 
visible,  which  have  not  been  injured  by  force,  are 
found  to  be  fnm  and  solid,  free  from  cracks  or  crev- 
ices, and  as  smooth  and  polished  on  the  surface  as 
when  first  applied.  The  sides  and  bottoms  of  the 
Roman  aqueducts  were  lined  with  this  plastering, 
and  endured  many  ages. 

At  Venice,  some  of  the  roofs  of  houses  and  the 
floors  of  rooms  are  covered  with  a  sort  of  plaster  of 
later  date,  and  yet  sti-ong  enough  to  endure  the  sun 
and  weather  for  several  ages  without  either  cracking 
or  spoiling. 

The  method  of  making  the  Venetian  composition 
is  not  known  in  England ;  but  such  might  probably 
be  made  by  heating  the  powder  of  gypsum  over  a 
fire,  and  when  boiling,  which  it  wUl  do  without  the 
aid  of  water  or  other  fluid,  mixing  it  with  rosin,  or 
pitch,  or  both  together,  with  common  sulphur,  and 
the  powder  of  sea  shells.  K  these  be  mbced  together, 
water  added  to  it,  and  the  composition  kept  on  the 
fire  till  the  instant  of  its  being  used,  it  is  not  improb- 
able that  the  secret  may  be  discovered.  Oil  of  tur- 
pentmc  and  wax,  which  are  the  common  ingredients 
in  such  cements  as  are  accounted  firmest,  may  also 
be  tried  as  additions,  as  also  may  strong  alewort, 
which  is  by  some  directed  to  be  used  instead  of 
water,  to  make  mortar  of  limestone  of  more  than 
ordinary  strength. 


SLATING. 

This  branch  of  building,  which  is  principally  em- 
ployed in  the  covering  of  roofs,  is  not  unfi-equently 
combined  with  that  of  plastering.  The  slates  chiefly 
used  in  London  are  brought  from  the  quarries  at 
Bangor,  in  Cacrnarvonshii-e,  which  supply  all  parts 
of  the  United  Kingdom.  Another  kind  of  slate,  of 
a  pale  blue-gi-een  color,  is  used,  and  most  esteemed, 
being  brought  from  Kendal,  in  Westmoreland,  called 
Westmoreland  slates.  These  slates  are  not  large,  but 
of  good  substance,  and  weU  calculated  to  give  a  neat 
appearance  to  a  roof  The  Scottish  slate,  which  as- 
similates in  size  and  quality  to  a  slate  from  Wales, 
called  ladies,  is  in  little  repute. 

The  slates  produced  in  this  country  are  principally 
from  the  quarries  in  the  State  of  Vermont.     In  point 


158 


BUILDING. 


of  durability,  they  are  equal  to  the  Welsh  slates,  but 
have  not  that  uniformity  of  color  which  distinguishes 
the  latter. 

The  height  of  roofs  at  the  present  time  is  very 
rarely  above  one  third  of  the  sjian,  and  should  never 
be  less  than  one  sixth.  The  most  usual  pitch  for 
slates  is  that  when  the  height  is  one  foiu'th  of  the 
span,  or  at  an  angle  of  26i  degrees  with  the  horizon. 
Taking  this  as  a  standard,  the  following  table  vn\l 
show  the  degree  of  inclination  which  may  be  given 
for  other  materials :  — 


Kind  of  Covering. 

Inclination 
to  tlie  hori- 
zon. 

Height     of 

roof  in  parts 

of  span. 

Weiglit 

upon  a  square 

of  roofing. 

Copper,       .     .     . 

. 

3  50 

A 

100 

Lead,     .... 

3  50 

-r'^ 

700 

Slates,  large,  .     . 

22  00 

Iff 

J, 

5 

1120 

Slates,  ordinary, 

.     . 

26  33 

1 
f 

From  900 
to     500 

Stone  slate,     .     . 

• 

29  41 

2380 

Plain  tiles,       .     . 

.     . 

29  41 

-? 

1780 

Pan  tiles,    .    .     . 

.     , 

24  00 

2 

650 

Thatch  of  straw  or  i 

eeds, 

45  00 

i 

Slaters  class  the  "^ 

kVelsh 

and  America) 

1  slates  in 

the  following  order : 

— 

Doubles,          averag 

e  size 

Ft.       In. 

11        b 

Ft.      In 

y         0     6 

Ladies,                  " 

a 

1    3 

0    8 

Countesses,          " 

(1 

1    8 

0  10 

Duchesses,            " 

u 

2    0 

1     0 

Welsh  rags,          " 

a 

3    0 

2    0 

Queens,                 '' 

(( 

3    0 

'         2    0 

Imperials,              " 
Patent  slate,         « 

11 

2 
2 

6 
6 

2    0 
2    0 

The  doubles  are  made  from  fragments  of  the  larger 
kinds,  and  derive  their  name  from  their  diminutive 
size.  Ladies  are  similarly  obtained.  Countesses  are 
a  gradation  above  ladies ;  and  duchesses  above  coun- 
tesses. 

Slate,  like  most  other  stony  substances,  is  separat- 
ed from  its  bed  by  the  ignition  of  gunpowder.  The 
blocks  thus  obtained  arc,  by  the  application  of  wedges, 
reduced  into  layers,  called  scantling-s,  from  four  to 
nine  inches  in  thickness,  and  of  any  requked  length 
and  breadth,  which  are  afterwards  sawed  to  the  re- 
spective sizes  by  raachmery.     The  blue,  green,  and 


for  buildings 
stables,  and  other 


purple,  or  darker  kinds  of  slate,  are,  in  general,  found 
capable  of  being  split  into  very  thin  laminae,  or  sheets ; 
but  those  of  the  white  or  brownish  freestone  land  can 
seldom  be  separated  or  divided  so  fine  ;  consequently, 
these  last  form  heavy,  strong,  thick  coverings,  proper 
in  exposed  situations,  siich  as  barns, 
outhouses. 

The  instruments  used  in  splitting  and  cleaning 
slates  are  slate  knives,  axes,  bars,  and  wedges ;  the 
three  first  being  vised  to  reduce  the  slates  into  the 
required  thicknesses,  and  the  last  to  remove  the  ine- 
qualities from  the  siuface. 

Imperial  slating  is  particularly  neat,  and  may  be 
known  by  having  its  lower  edge  sawed ;  whereas,  all 
other  slates  used  for  covering  are  chipped  square  on 
their  edges  only. 

Patent  slate  was  first  brought  into  use  by  Mr. 
Wyatt,  the  architect;  but  a  patent  was  never  ob- 
tained. It  derives  its  name  from  the  mode  adopted 
to  lay  it  on  the  roofs ;  it  may  be  laid  on  a  rafter  of 
much  less  elevation  than  any  other,  and  is  considera- 
bly lighter,  by  reason  of  the  laps  being  less  than  is 
necessary  for  the  common  sort  of  slating.  This  slat- 
ing was  originally  made  from  Welsh  rag-s ;  but  it  is 
now  very  frequently  made  from  imperials,  which  ren- 
der it  lighter,  and  also  somewhat  neater  in  appearance. 

Westmoreland  slate,  from  the  experiments  made  by 
the  late  Bishop  of  LlandafT,  appears  to  differ  a  little 
in  its  natural  composition  from  that  obtained  from 
Wales.  It  must,  however,  be  remarked,  that  this 
kind  of  slate  owes  its  lightness,  not  so  mucli  to  any 
diversity  in  the  component  parts  of  the  stone,  as  to 
the  thinness  to  which  it  is  reduced  by  the  workman  ; 
consequently,  it  is  not  so  well  calculated  to  resist 
violent  winds  as  those  which  are  heavier. 

Slates,  when  brought  from  the  quarry,  are  not  suf- 
ficiently square  for  the  slater's  use ;  he  therefore 
picks  up  and  examines  the  slates  separately,  and 
observes  Avhich  is  the  sti-ongest  and  squarest  end; 
then,  seating  himself,  he  holds  the  slate  a  little  slant- 
ing upon,  and  projecting  about  an  inch  over,  the 
edge  of  a  small  block  of  wood,  which  is  of  the  same 
height  as  his  scat,  and  cuts  away  and  makes  straight 
one  of  its  edges ;  then,  with  a  slip  of  wood,  he 
gauges  and  cuts  off  the  other  edge  parallel  to  it,  and 
squares  the  end.  The  slate  is  now  considered  pre- 
pared for  use,  with  the  exception  of  perforating 
through  its  opposite  ends  two  small  holes  for  the 
reception  of  the  nails  which  are  to  confine  it  to  the 


BUILDING. 


159 


roof.  Copper  and  zinc  nails,  or  iron  nails  tinned,  arc 
considered  the  best,  being  less  susceptible  of  oxida- 
tion than  nails  made  of  bar  iron. 

Before  we  proceed  fiu-thcr  with  the  operations 
necessary  in  the  slating  of  buildings,  we  shall  give 
some  account  of  the  tools  used  by  this  class  of  ar- 
tificers. 

Slaters'  tools  are  very  few,  whicli  sometimes  are 
found  by  the  masters,  and  sometimes  by  the  men. 
The  tool  called  the  saixe  is  made  of  tempered  iron, 
about  sixteen  inches  in  length,  somewhat  bent  at  one 
end,  with  a  handle  of  wood  at  the  other.  This  tool 
is  not  unlilcc  a  large  knife,  except  that  it  has  on  its 
back  a  projecting  piece  of  iron,  about  three  inches  in 
length,  drawn  to  a  sharp  point.  This  tool  is  used  to 
chip  or  cut  all  the  slates  to  the  required  sizes. 

The  ripper  is  also  of  iron,  about  the  same  length 
as  the  saixe ;  it  has  a  very  thin  blade,  about  an  inch 
and  three  quarters  wide,  tapered  somewhat  towards 
the  top,  where  a  round  head  projects  over  the  blade 
about  half  an  inch  on  each  side;  it  has  also  two 
little  round  notches  in  the  two  internal  angles,  at 
their  intersections.  The  handle  of  this  tool  is  raised 
above  the  blade  by  a  shoulder,  which  enables  the 
workman  to  hold  it  firm.  This  instrument  is  used 
in  repau-ing  old  slating,  and  the  application  consists 
in  thrusting  the  blade  under  the  slates,  so  that  the 
head,  which  projects,  may  catch  the  naU  in  the  little 
notch  at  its  intersection,  and  enable  Lhe  workman  to 
di-aw  it  out.  During  this  operation,  the  slate  is  suffi- 
ciently loosened  to  allow  of  its  beuig  removed  and 
another  inserted  in  its  place. 

The  hammer,  which  is  somewhat  different  in  shape 
to  the  ordinary  tool  of  that  name,  is  about  five  inches 
in  height  on  the  hammer  or  driving  part,  and  the  top 
is  bent  back,  and  gi'ound  to  a  tolerably  sharp  point, 
its  lower  or  flat  end,  which  is  quite  round,  being 
about  three  quarters  of  an  inch  in  diameter.  On 
this  side  of  the  di-iving  part  is  a  small  projection, 
with  a  notch  in  the  centre,  which  is  used  as  a  claw 
to  extract  such  nails   as  do  not  drive  satisfactorily. 

The  shaving  tool  is  used  for  getting  the  slates  to  a 
smooth  face  for  skirtings,  floors  for  balconies,  &c.  It 
consists  of  an  iron  blade,  sharpened  at  one  of  its 
ends  like  a  chisel,  and  mortised  through  the  centre 
of  two  round  wooden  handles,  one  fixed  at  one  end, 
and  the  other  about  the  middle  of  the  blade.  The 
blade  is  about  eleven  inches  long  and  two  inches 
wide,  and  the  handle  is  about  ten  inches  long ;   so 


that  they  project  about  four  inches  on  each  side  of 
the  blade.  In  using  this  tool,  the  workman  places 
one  hand  on  each  side  of  the  handle  that  is  in  the 
middle  of  the  blade,  and  allows  tlie  other  to  press 
against  both  his  wrists.  In  this  manner,  he  removes 
all  the  uneven  parts  from  off  the  face  of  the  slate, 
and  gets  it  to  a  smooth  surface. 

The  other  tools  used  by  the  slater  consist  of  chisels, 
gouges,  and  files  of  all  sizes  ;  by  means  of  which  he 
finishes  the  slates  into  mouldings  and  other  required 
forms. 

Li  slating  roofs,  it  is  necessary  to  form  a  base  or 
floor  for  the  slates  to  lay  compactly  and  safely  upon ; 
for  doubles  and  ladies,  boarding  is  requii-ed,  which 
must  be  laid  very  even,  with  the  joints  close,  and 
properly  secm-ed  by  nails  to  the  rafters.  This  being 
completed,  the  slater  provides  himself  with  several 
slips  of  wood,  called  tilling  fdlets,  about  ten  inches 
and  a  half  wide,  and  three  quarters  of  an  inch  thick 
on  one  edge,  and  chamfered  to  an  arris  on  the  other, 
which  he  nails  down  all  round  the  extreme  edges  of 
the  roof,  beginning  with  the  hips,  if  any,  and  if  not, 
with  the  sides,  eaves,  and  ridge.  He  next  selects  the 
largest  of  the  slates,  and  arranges  them  regularly 
along  the  eaves,  with  their  lower  edges  to  a  line,  and 
naUs  them  to  the  boarding.  This  part  of  the  work 
being  completed,  he  takes  other  slates  to  form  the 
bond  to  the  under  sides  of  the  eaves,  and  places 
them  under  those  previously  laid,  so  as  to  cross  and 
cover  aU  their  joints.  Such  slates  are  pushed  up 
lightly  under  those  which  are  above  them,  and  are 
seldom  nailed,  but  left  dependent  for  support  on  the 
weight  of  those  above  them,  and  then*  own  weight 
on  the  boarding.  The  countesses  and  all  other  de- 
scriptions of  slates,  when  intended  to  be  laid  in  a 
good  manner,  are  also  laid  on  boards. 

When  the  slater  has  finished  the  eaves,  he  stretches 
a  line  on  the  face  of  the  upper  slates,  parallel  to  its 
outer  edge,  and  as  far  from  it  as  he  deems  sufficient 
for  the  lap  of  those  he  intends  shall  form  the  next 
course,  which  is  laid  and  nailed  even  with  the  line, 
crossing  the  joints  of  the  upper  slates  of  the  eaves. 
This  lining  and  laying  is  continued  close  to  the  ridge 
of  the  roof,  observing  throughout  to  break  the  differ- 
ent joints,  by  laying  the  slates  one  above  another. 
The  same  system  is  universally  followed  in  laying  aU 
the  different  sorts  of  slates,  with  the  exception  of 
those  called  patent  slates,  as  hereafter  explained 

The  largest  kind  of  slates  are  found  to  lay  firm  on 


160 


BUILDING. 


battens,  which  are,  consequently,  much  employed, 
and  produce  a  very  considerable  saving  of  expense 
in  large  buildings.  A  batten  is  a  narrow  portion  of 
board,  about  two  inches  and  a  half  or  three  inches 
wide,  four  of  them  being  commonly  procm'ed  from 
an  eleven-inch  board. 

For  countess  slates,  battens  three  quarters  of  an 
inch  thick  will  be  of  adequate  substance  ;  but  for 
the  larger  and  heavier  kinds,  inch  battens  will  be 
necessary.  In  battening  a  roof  for  slates,  the  battens 
are  not  placed  at  a  uniform  distance  from  each  other, 
but  so  as  to  suit  the  length  of  the  slates ;  and  as 
these  vary  as  they  approach  the  apex  or  ridge  of  the 
roof,  it  follows  that  the  slater  himself  is  the  best 
judge  where  to  fix  them,  so  as  best  to  support  the 
slates. 

A  roof,  to  be  covered  with  patent  slates,  requh-es 
that  the  common  rafters  be  left  loose  upon  then-  pur- 
lines,  as  they  must  be  so  arranged  that  a  rafter  shall 
lie  under  every  one  of  the  meeting  joints.  Neither 
battening  nor  boarding  is  required  for  these  slates. 
The  number  of  rafters  will  depend  on  the  width  of 
the  slates ;  hence,  if  they  be  of  a  larger  size,  very 
few  will  suffice.  This  kind  of  slating  is  likewise 
commenced  at  the  eaves ;  but  no  crossing  or  bond- 
ing is  required,  as  the  slates  arc  laid  uniformly,  with 
each  end  reaching  to  the  centre  of  the  rafter,  and 
butted  up  to  each  other  throughout  the  length  of  the 
roof.  When  the  eaves-course  is  laid,  the  slates  which 
compose  it  are  screwed  down  to  the  rafters  by  two  or 
three  strong  inch  and  half  screws  at  each  of  then- 
ends.  A  line  is  then  sti-ained  about  two  inches  be- 
low the  upper  edge,  in  order  to  guide  the  laying  of 
course,  which  is  laid  with  its  lower  edge 


the  next 
touching 


the  line.  This  lining,  layhig  with  a  lap, 
and  screwing  down,  is  continued  till  the  roof  is  com- 
pletely covered.  The  joints  are  then  secured  by  fil- 
leting, which  consists  in  covering  all  tlic  meeting 
joints  with  fillets  of  slate,  bedded  in  glaziers'  putty, 
and  screwed  down  through  the  whole  into  the  rafters. 
The  fillets  are  usually  about  three  inches  wide,  and 
of  a  length  proportionate  to  that  of  the  slates  whose 
joints  they  have  to  cover.  These  fillets  are  solidly 
bedded  in  the  putty,  and  their  intersecting  joints  are 
lapped  similar  to  those  of  the  slates.  The  fillets 
being  so  laid,  and  secm-cd  by  one  in  the  middle  of 
the  fillet,  and  one  in  each  lap,  arc  next  neatly  pointed 
all  round  their  edges  with  more  putty,  and  then 
painted  over  with  the  color  of  the  slate.     The  hips 


and  ridges  of  such  slating  are  frequently  covered  by 
fillets,  which  produce  a  very  neat  effect ;  but  lead, 
which  is  not  much  dearer,  is  by  far  the  best  kind  of 
covering  for  all  hips  and  ridges.  The  patent  slating 
may  be  laid  so  as  to  be  perfectly  water  tight,  with 
an  elevation  of  the  rafters  considerably  less  than  for 
any  other  slate  or  tile  covering.  The  rise  in  each 
foot  of  length  in  the  rafter  is  not  required  to  be  more 
than  t«-o  inches,  which,  in  a  rafter  of  fifteen  feet,  will 
amount  to  only  two  feet  six  inches  —  a  rise  scarcely 
perceptible  from  the  gi-ound. 

Slating  is  performed  in  several  other  ways,  but  the 
prmciples  aheady  explained  embrace  the  most  of 
them.  Some  workmen  shape  and  lay  their  slates  in 
a  lozenge  form.  This  kind  of  work  consists  in  get- 
ting all  the  slates  to  a  uniform  size,  of  the  shape  of  a 
geometrical  square.  When  laid  on  the  roof,  which 
must  be  boarded,  they  are  bonded  and  lapped  as  in 
common  slating,  observing  only  to  let  the  elbow,  or 
half  of  the  square,  appear  above  each  slate  that  is 
next  beneath  it,  and  be  regular  in  the  courses  all  over 
the  roof.  One  naU  or  screw  only  can  be  used  for 
such  slating;  hence  it  soon  becomes  dOapidated.  It 
is  commonly  employed  in  places  near  to  the  eye,  or 
where  particular  neatness  is  required. 

It  has  been  ascertained  that  a  slate  one  inch  thick 
will,  in  a  horizontal  position,  support  as  much  in 
weight  as  five  inches  of  Portland  stone  similarly  sus- 
pended. Hence  slates  are  now  ^^^.■ought  and  used  in 
galleries,  and  other  pm'poses,  where  it  is  essential  to 
have  strength  and  lightness  combmed.  Slates  are 
also  fashioned  into  chimney-pieces,  but  arc  incapable 
of  receiving  a  polish  like  marble.  It  makes  excellent 
sku'tings  of  all  descriptions,  as  weU  as  casings  to 
walls,  where  dilapidations  or  great  wear  and  tear  are 
to  be  expected.  For  these  purposes,  it  is  capable  of 
being  fLxed  with  joints,  equally  as  neat  as  wood ;  and 
may,  if  required,  be  painted  over  so  as  to  appear  like 
it.  Staircases  may  also  be  executed  in  slate,  which 
vrill  produce  a  resemblance  of  marble. 


PLUMBING. 

Plumbing  is  the  art  of  casting  and  working  in 
lead,  and  using  the  same  in  the  covering  and  for 
other  purposes   in  building. 

To  the  plumber  is  also  confided  the  pump  work, 


BUILDING. 


161 


,  as  well  as  the  making  and  forming  of  cisterns  and 
reservoirs,  large  or  small  closets,  &c.,  for  the  purposes 
of  domestic  economy.  The  plumber  does  not  use  a 
great  variety  of  tools,  because  the  ductility  of  the 
metal  upon  which  he  operates  does  not  require  it. 
The  tools  used  consist  of  an  iron  hammer,  rather 
heavier  than  a  carpenter's,  with  a  short,  tliick  handle  ; 
two  or  three  wooden  mallets  of  different  sizes,  and  a 
Iressing  and  flatting  tool.  Tliis  last  is  of  beech, 
about  eighteen  inches  long  and  two  inches  square, 
planed  smooth  and  flat  on  the  under  surface,  and 
fouiaded  on  the  upper,  and  one  of  its  ends  tapered 
off  round  as  a  handle.  With  this  tool  he  stretches 
out  and  flattens  the  sheet  lead,  or  dresses  it  to  the 
shape  required,  using  first  the  flat  side,  then  the  round 
one,  as  occasion  may  require. 

The  plumber  has  also  occasion  for  a  jack  and 
trying  plane,  similar  to  that  of  the  carpenter.  With 
this  he  reduces  the  edges  of  sheet  lead  to  a  straight 
line,  when  the  purposes  to  which  it  is  to  be  applied 
require  it.  His  cutting  tools  consist  of  a  variety  of 
chisels  and  gouges,  as  well  as  knives.  The  latter  of 
these  are  used  for  cutting  the  sheet  lead  into  slips 
and  pieces  after  it  has  been  marked  out  by  the  chalk 
line. 

Files  of  difierent  sizes ;  ladles  of  three  or  four  sizes, 
for  melting  the  solder ;  and  an  iron  instrument  called 
g-rozing  irons. 

These  grozing  irons  are  of  several  sizes,  generally 
about  twelve  inches  in  length,  tapered  at  both  ends, 
the  handle  end  being  turned  quite  round,  to  allow 
of  its  being  firmly  held  whUe  in  use ;  the  other  end 
is  a  bulb,  of  a  spindle  or  spherical  shape,  of  a  size 
proportioned  to  the  soldering  intended  to  be  ex- 
ecuted. They  are,  when  required  for  use,  heated  to 
redness. 

The  plumber's  measm-ing  ride  is  two  feet  iii  length, 
divided  into  three  equal  parts  of  eight  inches  each ; 
two  of  its  legs  are  of  boxwood,  duodecimally  divided ; 
and  the  third  consists  of  a  piece  of  slow-tempered 
^teel,  attached  to  one  of  the  box  legs  by  a  pivot  on 
which  it  turns,  and  falls,  when  not  in  use,  into  a 
groove  cut  in  such  leg  for  its  reception.  This  steel 
leg  can  be  passed  into  places  where  the  others  can- 
not enter;  and  it  is  also  useful  for  occasionally  re- 
moving the  oxide  or  any  extraneous  matters  from  the 
surface  of  the  heated  metal. 

Scales  and  weights  are  also  necessary ;  and  he 
must  be  supplied  with  centre  bits  of  all  sizes,  for  the 

21 


purpose  of  making  perforations  in  lead  or  Wood, 
through  which  he  may  want  to  insert  pipes,  &c. 
Compasses,  to  strike  curcular  pieces,  to  line  or  cover 
figures  of  that  shape,  are  occasionally  required. 

Lead  is  obtained  from  ore,  and,  from  its  being  gen- 
erally combined  with  sulphur,  it  has  been  denomi- 
nated sulphuret.  After  the  ore  has  been  taken  from 
its  bed  it  is  smelted,  fust  being  picked,  in  order  to 
separate  the  unctuous  and  rich  or  genuine  ore  from 
the  stony  matrice,  and  other  impurities ;  the  picked 
ore  is  then  pounded  under  stampers  worked  by  ma- 
chinery, and  afterwards  washed  to  carry  off  the  re- 
mainder of  the  matrice,  which  could  not  be  separated 
in  picking.  It  is  next  put  into  a  reverberatory  fur- 
nace to  be  roasted ;  during  which  operation  it  is  re- 
peatedly stirred,  to  facilitate  the  evaporation  of  the 
sulphur.  When  the  surface  begins  to  assume  the 
appearance  of  a  paste,  it  is  covered  with  charcoal, 
and  well  shaken  together ;  the  fire  is  then  increased, 
and  the  purified  lead  flows  down  on  all  sides  into 
the  basin  of  the  furnace,  whence  it  runs  off  into 
moulds  prepared  for  its  reception.  The  moulds  are 
capable  of  receiving  one  hundi-ed  and  fifty -four  pounds 
of  lead  each,  and  their  contents,  when  cool,  are,  in 
the  commercial  world,  called  pigs. 

Lead  is  of  a  bluish-white  color,  and  when  newly 
melted,  or  cut,  is  quite  bright ;  but  it  soon  becomes 
tarnished  on  exposure  to  the  atmosphere  —  assuming 
first  a  dirty,  gray  color,  and  afterwards  becomes  white. 
It  is  capable  of  being  hammered  into  very  thin  plates, 
and  may  be  drawn  into  wire  ;  but  its  tenacity  is  very 
inferior  to  that  of  other  metals,  for  a  leaden  wire,  the 
hundred  and  twentieth  part  of  an  inch  in  diameter, 
is  only  capable  of  supporting  about  eighteen  pounds 
without  breaking.  Lead,  next  to  tin,  is  the  most  fu- 
sible of  all  metals ;  and  if  a  stronger  heat  be  applied,  it 
boils  and  evaporates.  If  cooled  slowly,  it  crystallizes. 
The  change  of  its  external  color  is  owing  to  its 
gradual  combination  with  oxygen,  which  converts  its 
exterior  surface  into  an  oxide.  This  outward  crust, 
however,  preserves  the  rest  of  the  metal  for  a  long 
time,  as  the  air  can  penetrate  but  very  slowly. 

Lead  is  not  acted  upon  immediately  by  water, 
though  that  element  greatly  facilitates  the  action  of 
the  air  upon  it ;  for  it  is  known  that,  when  lead  is 
exposed  to  the  atmosphere,  and  kept  constantly  wet, 
the  process  of  oxidation  takes  place  much  more  rap- 
idly than  it  does  under  other  circumstances ;  hence 
the  white  crust  that  is  to  be  obser\'ed  on  the  sides  of 


162 


BUILDING. 


leaden  vessels  containing  water,  just  at  the  place 
where  the  surface  of  the  water  terminates. 

Lead  is  piurchased  by  plumbers  in  pigs,  and  they 
reduce  it  into  sheets,  or  pipes,  as  they  have  occasion. 
Of  sheet  lead  they  have  two  kinds,  cast  and  milled. 
The  former  is  used  for  covering  flat  roofs  of  build- 
ings, laying  of  terraces,  forming  gutters,  lining  reser- 
voirs, &c. ;  and  the  latter,  which  is  very  thin,  for  cov- 
ering the  hips  and  ridges  of  roofs.  This  last  they  do 
not  manufacture  themselves,  but  purchase  it  of  the 
lead  merchants,  ready  prepared. 

For  the  casting  of  sheet  lead,  a  copper  is  provided, 
and  well  fixed  in  masonry,  at  the  upper  end  of  the 
workshop,  near  the  mould  or  casting  table,  which 
consists  of  strong  boards,  well  jointed  together,  and 
bound  with  bars  of  iron  at  the  ends.  The  sides  of 
this  table,  of  which  the,  shape  is  a  parallelogram,  vary 
in  size  from  four  to  six  feet  in  width,  and  from  six- 
teen to  eighteen  feet  and  upwards  in  length,  and  are 
guarded  by  a  frame  or  edging  of  wood,  three  inches 
thick,  and  four  or  five  inches  higher  than  the  interior 
surface,  called  the  shafts.  This  table  is  fixed  upon 
firm  legs,  strongly  framed  together,  about  sLs  or  seven 
inches  lower  than  the  top  of  the  copper.  At  the  up- 
per end  of  the  mould,  nearest  the  copper,  is  a  box, 
called  the  pan,  which  is  adapted  in  its  length  to  the 
breadth  of  the  table,  having  at  its  bottom  a  long,  hor- 
izontal slit,  from  which  the  heated  metal  is  to  issue, 
when  it  has  been  poured  in  from  the  copper.  This 
box  moves  upon  rollers  along  the  surface  of  the  rim 
of  the  table,  and  is  put  in  motion  by  means  of  ropes 
and  pulleys,  fixed  to  beams  above.  While  the  metal 
is  melting,  the  surface  of  the  mould,  or  table,  is  pre- 
pared by  covering  it  with  a  stratum  of  dry  and  clean 
sand,  regularly  smoothed  over  with  a  kind  of  rake, 
called  a  strike,  which  consists  of  a  board  about  five 
inches  broad,  and  rather  longer  than  the  inside  of  the 
mould,  so  that  its  ends,  which  arc  notched  about  two 
inches  deep,  may  ride  upon  the  shafts.  This  being 
passed  down  the  whole  length  of  the  table,  reduces 
the  sand  to  a  uniform  surface.  The  pan  is  now 
brought  to  the  head  of  the  table,  close  to  the  copper, 
its  sides  having  previously  been  guarded  by  a  coat 
of  moistened  sand,  to  prevent  its  firing  from  the  heat 
of  the  metal,  which  is  now  put  in  by  ladles  from  the 
copper. 

These  pans,  or  boxes,  it  must  be  observed,  are  made 
to  contain  the  quantity  of  melted  lead  which  is  re- 
quired to  cast  a  whole  sheet  at  one  time  ;  and  the 


slit  in  the  bottom  is  so  adjusted  as  to  let  out,  during 
its  progress  along  the  table,  just  as  much  as  wUl  com- 
pletely cover  it  of  the  thickness  and  weight  per  foot 
required.  Every  thing  being  thus  prepared,  the  slit 
is  opened,  and  the  box  moved  along  the  table,  dis- 
pensing its  contents  from  the  top  to  the  bottom,  and 
leaving  in  its  progress  a  sheet  of  lead  of  the  desired 
thickness.  When  cool,  the  sheet  is  rolled  up  and 
removed  from  the  table,  and  other  sheets  are  cast, 
till  all  the  metal  in  the  copper  is  exhausted.  The 
sheets  thus  formed  are  then  rolled  up  and  kept  for  use. 

In  some  places,  instead  of  having  a  square  box 
upon  wheels,  with  a  slit  in  the  bottom,  the  pan  con- 
sists of  a  kind  of  trough,  being  composed  of  two 
planks  nailed  together  at  right  angles,  with  two  tri- 
angular pieces  fitted  in  between  them  at  their  ends. 
The  length  of  this  pan,  as  well  as  that  of  the  box,  is 
equal  to  the  whole  breadth  of  the  mould.  It  is  placed 
with  its  bottom  on  a  bench  at  the  head  of  the  table, 
leaning  with  one  side  against  it ;  to  the  opposite  side 
is  fixed  a  handle,  by  which  it  may  be  lifted  up  in  order 
to  pour  out  the  liquid  metal.  On  the  side  of  the  pan 
next  the  mould  are  two  iron  hooks,  to  hold  it  to  the 
table,  and  prevent  it  from  slipping  while  the  metal  is 
being  poured  into  the  mould. 

The  mould,  as  well  as  the  pan,  is  spread  over  about 
two  inches  thick  with  sand  sifted  and  moistened,  and 
rendered  perfectly  level  by  moving  over  it  the  strike, 
and  smoothing  it  down  with  a  plane  of  polished 
brass,  about  a  quarter  of  an  inch  thick  and  nine 
inches  square,  tiuned  up  on  the  edges. 

Before  they  proceed  to  casting  the  lead,  the  strike 
is  made  ready  by  tacking  two  pieces  of  old  hat  on  the 
notches,  or  by  covering  the  notches  with  leather 
cases,  so  as  to  raise  the  under  side  of  the  strike 
about  an  eighth  of  an  inch  or  more  above  the  sand, 
according  to  the  proposed  thickness  of  the  sheet. 
The  face  or  under  side  of  the  strike  is  then  smeared 
with  tallow,  and  laid  across  the  breadth  of  the  mould, 
with  its  ends  resting  on  the  shafts.  The  melted  lead 
is  then  put  into  the  pan  with  ladles ;  and,  when  a  . 
sufficient  quantity  has  been  put  in,  the  scum  is  swept 
off"  with  a  piece  of  board,  and  suffered  to  settle  on 
the  coat  of  sand,  to  prevent  its  falling  into  the  mould 
when  the  metal  is  poured  out.  It  generally  happens 
that  the  lead,  when  first  taken  from  the  copper,  is  too 
hot  for  casting ;  it  is,  therefore,  suffered  to  cool  in  the 
pan  till  it  begins  to  stand  with  a  shell  or  wall  on  the 
sand  with  which  the  pan  is  lined.     Two  men  ther 


BUILDING. 


163 


take  the  pan  by  the  handle,  or  one  of  them  takes  it 
by  means  of  a  bar  or  chain  fixed  to  a  beam  in  the 
ceiling,  and  turn  it  down,  so  that  the  metal  runs  into 
the  mould ;  while  another  man  stands  ready  with  the 
strike,  and,  as  soon  as  all  the  metal  is  poured  in, 
sweeps  it  forward  and  draws  the  residue  into  a 
trough  at  the  bottom,  which  has  been  prepared  to 
receive  it.     The  sheet  is    then    rolled  up  as  before. 

In  this  mode  of  operation,  the  table  inclines  in  its 
length  about  an  inch  or  an  inch  and  a  half,  in  the 
length  of  sixteen  or  seventeen  feet,  or  more,  accord- 
ing to  the  required  thickness  of  the  sheets :  the  thin- 
ner the  sheet,  the  greater  the  declivity ;  and  vice 
versa.  The  lower  end  of  the  mould  is  also  left  open, 
to  admit  of  the  superfluous  metal  being  thrown  off. 

When  a  cistern  is  to  be  cast,  the  size  of  the  four 
sides  is  measured  out;  and  the  dimensions  of  the 
front  having  been  taken,  slips  of  wood,  on  which  the 
mouldings  are  carved,  are  pressed  upon  the  sand. 
Figures  of  birds,  beasts,  &c.,  are  likewise  stamped  in 
the  internal  area,  by  means  of  leaden  moulds.  K 
any  part  of  the  sand  has  been  disturbed  in  doing 
this,  it  is  made  smooth,  and  the  process  of  casting 
goes  on  as  for  plain  sheets ;  except  that,  instead  of 
rolling  up  the  lead  when  cast,  it  is  bent  into  four 
sides,  so  that  the  two  ends,  when  they  are  soldered 
together,  may  be  joined  at  the  back :  the  bottom  is 
afterwards  soldered  up. 

The  lead  which  lines  the  Chinese  tea  boxes  is  re- 
duced to  a  thinness  which  our  plumbers  cannot,  it  is 
said,  approach.  The  following  account  of  the  pro- 
cess was  communicated  by  an  intelligent  East  Lidian, 
in  a  letter  which  appeared  in  the  Gentleman's  Mag- 
azine :  "  The  caster  sits  by  a  pot  containing  the 
melted  metal,  and  has  two  large  stones,  the  lower 
one  fixed  and  the  upper  one  movable,  having  their 
surfaces  of  contact  ground  to  each  other,  directly 
before  him.  He  raises  the  upper  stone  by  pressing 
his  foot  upon  its  side,  and  with  an  iron  ladle  pours 
into  the  opening  a  sufficient  quantity  of  the  fluid 
metal.  He  then  lets  fall  the  upper  stone,  and  thus 
forms  the  lead  into  an  extremely  thin  and  irregular 
plate,  which  is  afterwards  cut  into  its  required  form." 

Cast  sheet  lead,  used  for  architectural  purposes,  is 
technically  divided  into  5  lb.,  5^  lb.,  6  lb.,  6^  lb.,  7  lb., 
7A  lb.,  8  lb.,  and  S|  lb.;  by  which  is  understood 
that  every  superficial  foot  is  to  contain  those  respec- 
tive weights,  according  to  the  price  agreed  upon. 

The  milled  lead  used  by  plumbers  is  very  thin,  sel- 


dom containing  more  than  five  pounds  to  the  foot.  It 
is  by  no  means  adapted  to  gutters  or  terraces,  nor,  in- 
deed, to  any  part  of  a  building  that  is  much  exposed 
either  to  great  wear  or  to  the  effects  of  the  sun's  rays : 
in  the  former  case,  it  soon  wears  away ;  in  the  latter, 
expands  and  cracks.  It  is  laminated  in  sheets  of 
about  the  same  size  as  those  of  cast  lead,  by  means 
of  a  roller,  or  flatting  mill. 

Lead  pipes  are  sometimes  made  of  sheet  lead,  by 
beating  it  on  round  wooden  cylinders  of  the  length 
and  dimensions  required,  and  then  soldering  up  the 
edges. 

Solder  is  used  to  secure  the  joints  of  work  in  lead, 
which,  by  other  means,  would  be  impossible.  It 
should  be  easier  of  fusion  than  the  metal  intended  to 
be  soldered,  and  should  be  as  nearly  as  possible  of  , 
the  same  color.  The  plumber,  therefore,  uses  what 
is  technically  called  soft  solder,  which  is  a  compound 
of  equal  parts  of  tin  and  lead,  melted  together  and 
run  into  moulds.  In  this  state  it  is  sold  by  the 
manufacturer,  by  the  pound. 

In  the  operation  of  soldering,  the  surfaces  or  edges 
intended  to  be  united  are  scraped  very  clean,  and 
brought  close  up  to  each  other,  in  which  state  they 
are  held  by  an  assistant,  while  the  plumber  applies  a 
little  resin  on  the  joints,  in  Order  to  prevent  the  oxida- 
tion of  the  metal.  The  heated  solder  is  then  brought 
in  a  ladle  and  poured  on  the  joint ;  after  which  it  is 
smoothed  and  finished  by  rubbing  it  about  with  a 
red-hot  soldering  iron ;  when  completed,  it  is  made 
smooth  by  filing. 

Li  the  covering  of  roofs  or  terraces  with  lead,  (the 
sheets  never  exceeding  six  feet  in  breadth,)  it  be- 
comes necessary,  in  large  surfaces,  to  have  joints, 
which  are  managed  several  ways,  but  in  all  the  chief 
object  is  to  have  them  water  tight.  The  best  plan 
of  effecting  this  is  to  form  laps,  or  roll  joints,  which  is 
done  by  having  a  roU  or  strip  of  wood  about  two 
inches  square,  but  rounded  on  its  upper  side,  naile<J 
under  the  joints  of  the  sheets,  where  the  edges  lap 
over  each  other :  one  of  these  edges  is  to  be  dressed 
up  over  the  roll  on  the  inside,  and  the  other  is  to  be 
dressed  over  them  both  on  the  outside,  by  which 
means  the  water  is  prevented  from  penetrating.  No 
other  fastening  is  requisite  than  what  is  required 
from  the  hammering  of  the  sheets  together  down 
upon  the  flat ;  nor  should  any  other  be  resorted  to 
when  sheet  lead  is  exposed  to  the  vicissitudes  of  tho 
weather,  because  it  expands  and  shrinks,  which,  if 


164 


BUILDING. 


prevented  by  too  much  fastening,  would  cause  it  to 
crack  and  become  useless.  It  sometimes,  however, 
occurs,  that  rolls  cannot  be  used,  and  then  the  method 
of  joining  by  seams  is  resorted  to.  This  consists  in 
simply  bending  the  approximate  edges  of  the  lead 
up  and  over  each  other,  and  then  dressing  them  down 
close  to  the  flat,  throughout  their  length.  But  this  is 
not  equal  to  the  roll,  either  for  neatness  or  security. 

Lead  flats  and  gutters  should  always  be  laid  with 
the  current,  to  keep  them  dry.  About  a  quarter  of 
an  inch  to  the  foot  is  a  sufficient  inclination. 

In  laying  gutters,  &c.,  pieces  of  milled  lead,  called 
flushing-,  about  eight  or  nine  inches  wide,  are  fixed 
in  tlic  walls,  all  round  the  edges  of  the  sheet  lead, 
with  which  the  flat  is  covered,  and  are  suffered  to 
hang  down  over  them,  so  as  to  prevent  the  passage 
of  rain  through  the  interstice  between  the  raised 
edge  and  the  waU.  If  the  waUs  have  been  previously 
bmlt,  the  mortar  is  raked  out  of  the  joint  of  the 


bricks   next   above  the 


edge 


of  the  sheet,  and  the 


ffushings  are  not  only  inserted  into  the  crack  at  the 
upper  sides,  but  their  lower  edges  are  likewise  dressed 
over  those  of  the  lead  in  the  flat,  or  gutter.  When 
neither  of  these  modes  can  be  resorted  to,  the  flush- 
ings are  fastened  by  waU  hooks,  and  their  lower 
edges  dressed  down  as  before. 

Drips  in  flats,  or  gutters,  are  formed  by  raising  one 
part  above  another,  and  dressing  the  lead,  as  already 
described,  for  covering  the  rolls.  They  are  resorted 
to  when  the  gutter  or  flat  exceeds  the  length  of  the 
sheet;  or,  sometimes,  for  convenience.  They  are 
also  a  useful  expedient  to  avoid  soldering  the  joints. 

Sheet  lead  is  also  used  in  the  lining  of  reservoirs, 
which  are  made  either  of  wood  or  masonry.  As 
these  conveniences  are  seldom  in  places  subject  to 
material  changes  of  temperature,  recourse  may  be 
had  to  the  soldering  without  fear  of  its  damaging 
the  work,  by  promoting  a  disposition  to  crack. 

The  pumps  which  come  under  the  province  of  the 
plumber  are  confined  generally  to  two  or  three  kinds 
used  for  domestic  purposes,  of  which  the  suction  and 
lifting  pumps  arc  the  chief;  these,  as  well  as  water 
closets,  are  manufactured  by  a  particular  set  of  work- 
men, and  sold  to  the  plumber,  who  furnishes  the  lead 
pipes,  and  fixes  them  in  thek  places. 

Plumbers'  work  is  generally  estimated  by  the 
pound,  or  hundred  weight ;  but  the  weight  may  be 
discovered  by  measurement,  in  the  following  manner : 
Sheet  lead  used  in  roofing  and  guttering  is  commonly 
between   seven   and  twelve   pounds  to  the  square 


foot ;  but  the  following  table  exhibits  the  particular 
weight  of  a  square  foot  for  each  of  the  several 
thicknesses :  — 


.  Thickness. 

lbs.  to  a  sq.  foot. 

Thickness. 

lbs.  to  a  sq.  foot. 

.10 

5.899 

.15 

8.848 

.11 

6.489 

.16 

9.438 

i 

6.554 

i 

9.831 

.12 

7.078 

.17 

10.028 

■h 

7.-373 

.18 

10.618 

.13 

7.668 

.19 

11.207 

.14 

8.258 

1 

11.797 

i 

8.427 

.21 

12.387 

In  this  table,  the  thickness  is  set  down  in  tenths 
and  hundredths,  &c.,  of  an  inch ;  and  the  annexed 
corresponding  numbers  are  the  weights  in  avoirdu- 
pois pounds  and  xoVtt  of  a  pound ;  so  that  the 
weight  of  a  square  foot  of  ^d  in-  thick,  -^iP^,  is  5  i%^^a 
pounds ;  and  the  weight  of  a  square  foot,  }  in.  in 
thiclcness,  is  6  ^\^^  pounds.  Leaden  pipe,  of  an 
inch  bore,  is  commonly  thirteen  or  fourteen  pounds 
to  the  yard  in  lengtli. 


GLAZING. 

The  business  of  this  class  of  artificers  consists  in 
putting  glass  into  sashes  and  casements.  Glaziers' 
work  may  be  classed  under  three  distinct  heads  — 
sash  work,  lead  work,  and  fret  work. 

The  tools  requisite  for  the  performances  of  the 
first  of  these  departments  are,  a  diamond,  a  ranging 
lathe,  a  short  lathe,  a  square,  a  rule,  a  glazing  knife, 
a  cutting  chisel,  a  beading  hammer,  duster,  and  sash 
tool ;  and,  in  addition,  for  stopping  in  squares,  a 
hacking  knife  and  hammer. 

The  diamond  is  a  speck  of  that  precious  stone, 
polished  to  a  cutting  point,  and  set  in  brass  on  an 
iron  socket,  to  receive  a  wooden  handle,  which  is  so 
set  as  to  be  held  in  the  hand  in  the  cutting  direction. 
The  top  of  the  handle  goes  between  the  root  of  the 
forefinger  and  the  middle  finger,  and  the  hinder  part 
between  the  point  of  the  forefinger  and  thumb ;  there 
is,  in  general,  a  notch  in  the  side  of  the  socket,  which 
should  be  held  next  to  the  lathe.  Some  diamonds 
have  more  cuts  than  one.  Plough  diamonds  have  a 
square  nut  on  the  end  of  the  socket  next  the  glass, 
which,  on  running  the  nut  square  on  the  side  of  the 
lathe,  keeps  it  in  the  cutting  direction.  Glass  grinders 
have  these  plough  diamonds  without  long  handles, 


BUILDING. 


165 


as,  in  cutting  their  curious  productions,  they  cannot 
apply  a  lathe,  but  direct  them  by  the  point  of  their 
middle  finger,  gliding  along  the  edge  of  the  glass. 

The  ranging  lathe  must  be  long  enough  to  extend 
rather  beyond  the  boundary  of  the  table  of  glass. 

Ranging  of  glass  is  the  cutting  it  in  breadths  as 
the  work  may  require,  and  is  best  done  by  one  unin- 
terrupted cut  from  one  end  to  the  other. 

The  square  is  used  in  cutting  the  squares  from  the 
range,  that  they  may  with  greater  certainty  be  cut  at 
right  angles.  The  glazing  knife  is  used  for  laying 
in  the  putty  in  the  rabbets  of  the  sash,  for  binding 
in  the  glass,  and  for  finishing  the  front  putty. 

Of  the  glass  used  in  building,  tlu-ee  qualities  are  in 
common  use,  denominated  best,  second,  and  third. 
The  best  is  that  which  is  the  purest  metal  and  free 
of  blemishes,  as  blisters,  specks,  streaks,  &c. ;  the 
second  is  inferior,  from  its  not  being  so  free  from 
these  blemishes ;  and  the  third  is  still  inferior,  both 
in  regard  to  quality  and  color,  being  of  greener  hue. 
They  are  sold  at  the  same  price  per  crate  ;  but  the 
number  of  tables  varies  according  to  the  quality. 
Best  twelve,  second  fifteen,  and  third  eighteen 
tables. 

These  tables  are  circular  when  manufactured,  and 
about  4  feet  in  diameter,  having  in  the  centre  a  knot, 
to  which,  in  the  course  of  the  process,  the  flashing 
rod  was  fixed  ;  but  for  the  safety  of  carriage  and  con- 
venience of  handling,  as  well  as  utility  in  practice,  a 
segment  is  cut  off  about  4  inches  from  the  knot. 
The  large  piece  with  the  knot  still  retains  the  name 
of  table  ;  the  smaller  piece  is  technically  called  a  slab. 
From  these  tables  being  of  a  given  size,  it  is  reason- 
able to  suppose  that,  v.^hen  the  dimensions  of  squares 
are  such  as  cut  the  glass  to  waste,  the  price  should 
be  advanced. 

A  superior  kind  of  glass  may  be  obtained  at  some 
of  the  first  houses  in  London,  which  is  very  flat  and 
of  large  dimensions,  some  of  it  being  2  feet  8  inches 
by  2  feet  1  inch ;  these  are  sold  only  in  squares. 

Rough  glass  is  vv'ell  adapted  to  baths  and  other 
places  of  privacy ;  one  side  is  ground  with  emery  or 
sand,  so  that  no  objects  can  be  seen  through  it,  though 
the  light  be  still  transmitted. 

Plate  glass  is  the  most  superior  in  quality,  sub- 
stance, and  flatness,  being  cast  in  plates,  and  pol- 
ished. The  quantity  of  metal  it  contains  must  be 
almost,  if  not  altogether,  colorless;  that  sort  which  is 
tinged  being  of  an  inferior  quality.    Plate  glass,  when 


used  in  sashes,  is  peculiarly  magnificent ;  and  it  can 
be  had  of  larger  dimensions  than  any  other  Idnd  of 
glass. 

Stained  glass  is  of  diflerent  color,  as  red,  orange, 
yellow,  green,  blue,  and  purple.  These  colors  are 
fixed  by  burning,  and  are  as  durable  as  the  glass. 

La  this  country,  window  glass  is  iised  of  various 
sizes,  from  7  inches  by  9  inches  to  12  by  20  inches. 
It  is  packed  by  the  manufacturers  in  boxes,  contain- 
ing 50  or  100  square  superficial  feet.  There  are 
many  manufactories  of  this  article  in  the  United 
States  which  usually  produce  glass  of  good  quality ; 
but  the  reputation  of  Boston  plate  glass  stands  de- 
cidedly higher  than  any  other,  either  of  foreign  or 
domestic  manufacture.  The  "  New  England  Com- 
pany," in  Boston,  manufacture  stained  glass  in  a  style 
not  surpassed  in  Europe. 

Glass  can  be  bent  to  circular  sweeps,  which  is 
much  used  in  London  for  shop  windows,  and  is  car- 
ried to  great  perfection  in  covers,  for  small  pieces  of 
statuary,  &c. 

The  application  of  stained  glass  to  the  purposes 
of  glazing  is  called  fretwork.  This  description  of 
work  consists  of  working  ground  and  stained  glass, 
in  fine  lead,  into  different  patterns.  In  many  cases, 
family  arms  and  other  devices  are  worked  in  it.  It 
is  a  branch  capable  of  great  improvement,  but  at 
present  is  much  neglected.  Old  pieces  are  very  much 
esteemed,  though  the  same  expense  would  furnish 
elegant  modern  productions.  They  are  placed  in 
halls  and  stancase  windows,  or  in  some  particular 
chrurch  windows.  La  many  instances,  they  are  intro- 
duced where  there  is  an  unpleasant  aspect,  iia  a  place 
of  particular  or  genteel  resort. 

Lead  work  is  used  in  inferior  offices,  and  is  in 
general  practice  all  through  the  country.  Frames 
intended  to  receive  these  lights  are  made  with  bars 
across,  to  which  the  lights  are  fastened  by  leaden 
bars,  called  saddle  bars;  and  where  openings  are 
wanted,  a  casement  is  introduced  either  of  wood  or 
iron.  Sometimes  a  sliding  frame  answers  the  same 
purposes.  Church  windows  are  generally  made  in 
this  manner,  in  quaaTies  or  in  squares. 

The  tools  with  which  this  work  is  performed  are, 
in  addition  to  the  foregoing,  as  follows :  — 

A  vice,  with  different  cheeks  and  cutters,  to  turn 
out  the  different  lands  of  lead,  as  the  magnitude  of 
the  window  or  the  squares  may  requure. 


166 


BUILDING. 


The  German  vices,  which  are  esteemed  the  best, 
arc  furnished  with  moulds,  and  turn  out  lead  in  a 
variety  of  sizes.  The  bars  of  lead  cast  in  these  vices 
are  received  by  the  mUl,  which  turns  them  out  with 
two  sides  parallel  to  each  other,  and  about  f  of  an 
inch  broad,  witli  a  partition  connecting  the  two  sides 
together,  about  J  of  an  inch  wide,  forming  on  each 
side  a  groove,  nearly  |  by  ^  of  an  inch,  and  about  6 
feet  long. 

Besides  a  vice  and  moulds,  there  are  a  setting  board, 
latterkin,  setting  knife,  resin  box,  tin,  glazing  irons, 
and  clips. 

The  setting  board  is  tliat  in  which  the  ridge  of  the 
light  is  marked  and  divided  into  squares,  struck  out 
with  a  chalk  line,  or  drawn  with  a  lathe,  which  serves 
to  guide  the  workman.  One  side  and  end  is  squared 
with  a  projecting  bead  or  fillet. 

The  latterkin  is  a  piece  of  hard  wood  pointed,  to 
run  in  the  groove  of  the  lead,  and  widen  it  for  the 
easier  reception  of  the  glass. 

The  setting-  knife  consists  of  a  blade  with  a  round 
point,  loaded  with  lead  at  the  bottom,  and  termiiiat- 
ing  in  a  long,  square  handle.  The  square  end  of  the 
handle  serves  to  force  the  square  of  glass  tight  in  the 
lead.  All  the  intersections  are  soldered  on  both  sides, 
except  the  outside  joints  of  the  outer  sides  —  that  is, 
where  they  come  to  the  outer  edge.  These  lights 
should  be  cemented  by  pouring  thin  paint  along  the 
lead  bars,  and  filling  up  the  chasms  with  dry  whitmg, 
to  which,  after  the  oil  in  the  paint  has  secreted  a  lit- 
tle, a  little  more  dry  whiting,  or  white  lead,  must  be 
added.  This  will  dry  hard,  and  resist  the  action  of 
the  atmosphere. 


PAINTING. 

Painting,  as  applied  to  purposes  of  building,  is  the 
application  of  artificial  colors,  compounded  either 
with  oil  or  w^ater,  in  embellishing  and  preserving 
wood,  &c. 

This  branch  of  painting  is  termed  economical,  and 
applies  more  immediately  to  the  power  which  oil  and 
varnishes  possess,  of  preventing  the  action  of  the  at- 
mosphere upon  wood,  iron,  and  stucco,  by  interposing 
an  artificial  surface  ;  but  it  is  here  intended  to  use 
the  term  more  generally,  in  allusion  to  the  decorative 
part,  and  as  it  is  employed  by  the  architect,  throughout 
every  part  of  his  work,  both  externally  and  internally. 


In  every  branch  of  painting  in  oil,  the  general  pro- 
cesses are  very  similar,  or  with  such  variations  only 
as  readily  occur  to  the  workman. 

The  first  coatings,  or  layers,  if  on  wood  or  iron, 
ought  always  to  be  of  ceruse  or  white  lead,  of  the 
best  quality,  previously  ground  very  fine  in  nut  or 
linseed  oil,  either  over  a  stone  with  a  muUer,  or,  as 
that  mode  is  too  tedious  for  large  quantities,  passed 
through  a  mill.  If  used  on  shutters,  doors,  or  wain- 
scotings,  made  of  pine,  it  is  very  requisite  to  destroy 
the  effects  of  the  knots,  which  are  generally  so  com- 
pletely saturated  with  turpentine  as  to  render  it,  per- 
haps, one  of  the  most  difficult  processes  in  this  busi- 
ness. The  best  mode  in  common  cases  is  to  pass  a 
brush  over  the  knots  with  ceruse  ground  in  water, 
bound  by  a  size  made  of  parchment  or  glue ;  when 
that  is  dry,  paint  the  knots  with  white  lead  ground 
in  oil,  to  which  add  some  powerful  siccative,  or  drier, 
as  red  lead,  or  litharge  of  lead  ;  about  one  part  of  the 
latter.  These  must  be  laid  very  smoothly  in  the  di- 
rection of  the  grain  of  the  wood. 

When  the  last  coat  is  dry,  smooth  it  with  pumice 
stone,  or  give  it  the  first  coat  of  paint,  prepared  or 
diluted  with  nut  or  linseed  oil;  after  which,  when 
sufficiently  dry,  all  the  nail  holes  or  other  irregulari- 
ties on  the  surface  must  be  carefully  stopped  with  a 
composition  of  oil  and  Spanish  white,  commonly 
known  by  the  name  of  putty.  The  work  must  then 
be  painted  with  white  lead  and  oil,  somewhat  diluted 
with  the  essence  of  oil  of  turpentine,  which  process 
should,  if  the  work  be  intended  to  be  left  of  a  plain 
white  or  stone  color,  be  repeated  not  lessi  than  three 
or  four  times ;  and  if  of  the  latter  color,  a  small  quan- 
tity of  ivory  or  lampblack  should  be  added.  But  if 
the  work  is  to  be  finished  of  any  other  color,  either 
gray,  green,  &c.,  it  will  be  requisite  to  provide  for 
such  color  after  the  third  operation,  particularly  if  it 
is  to  be  finished  flat,  or,  as  the  painters  style  it,  dead 
white,  gray,  fawn,  &c.  Li  order  to  finish  the  work 
flatted  or  dead,  which  is  a  mode  much  to  be  preferred 
for  all  superior  works,  not  only  for  its  appearance,  but 
also  for  preserving  the  color  and  pm-ity  of  the  tint, 
one  coat  of  the  flatted  color,  or  color  mixed  up  with 
a  considerable  quantity  of  turpentine,  will  be  found 
sufficient ;  although  in  large  surfaces  it  will  be  fre- 
quently requisite  to  give  two  coats  of  the  flatting 
color  to  make  it  quite  complete.  Indeed,  on  stucco 
it  will  be  almost  a  general  rule. 

In  all  the  foregoing  operations,  it  must  be  observed 


BUILDING. 


167 


that  some  sort  of  drier  is  absolutely  requisite ;  a  very 
general  and  useful  one  is  made  by  grinding  in  lin- 
seed, or  perhaps  prepared  oils,  boiled,  are  better,  about 
two  parts  of  the  best  white  copperas,  which  must  be 
well  dried  with  one  part  of  litharge  of  lead ;  the  quan- 
tity to  be  added  will  much  depend  on  the  dryness  or 
humidity  of  the  atmosphere  at  the  time  of  painting, 
as  well  as  the  local  situation  of  the  building.  It  may 
here  be  noticed,  that  there  is  a  sort  of  copperas  made 
in  England,  and  said  to  be  used  for  some  purposes 
in  medicine,  that  not  only  does  not  assist  the  opera- 
tion of  drying  in  the  colors,  but  absolutely  prevents 
these  colors  drying,  which  would  otherwise  have  done 
BO  in  the  absence  of  the  copperas. 

The  best  drier  for  all  fine  whites  and  other  deli- 
cate tints  is  sugar  of  lead,  ground  in  nut  oil ;  but  be- 
ing very  active,  a  small  quantity,  about  the  size  of  a 
walnut,  \\dll  be  sufficient  for  twenty  pounds  of  color, 
when  the  basis  is  white  lead. 

It  does  not  appear  that  painting  in  oil  can  be  ser- 
viceable in  stucco,  unless  the  walls  have  been  erected 
a  sufficient  time  to  permit  the  mass  of  brick  work  to 
have  acquired  a  sufficient  degree  of  dryness.  When 
stucco  is  on  battened  work,  it  may  be  painted  over 
much  sooner  than  when  prepared  on  brick.  Indeed, 
the  greatest  part  of  the  art  of  painting  stucco,  so  as 
to  stand  or  wear  well,  consists  in  attending  to  these 
observations ;  for  whoever  has  observed  the  expan- 
sive power  of  water,  not  only  in  congelation,  but  also 
in  evaporation,  must  be  well  aware  that  when  it 
meets  with  any  foreign  body  obstructing  its  escape, 
as  oil  painting,  for  instance,  it  immediately  resists  it, 
forming  a  number  of  vesicles  or  particles,  containing 
an  acrid  lime  water,  which  forces  off  the  layers  of 
plaster,  and  frequently  causes  large  defective  patches, 
not  easily  to  be  eradicated. 

Perhaps  in  general  cases,  where  persons  are  build- 
ing on  their  own  estates  or  for  themselves,  two  or 
three  years  are  not  too  long  to  suffer  the  stucco  to 
remain  unpainted,  though  frequently,  in  speculative 
works,  as  many  weeks  are  scarcely  allowed  to  pass. 

The  foregoing  precautions  being  attended  to,  there 
can  be  no  better  mode  adopted  for  priming,  or  laying 
on  the  first  coat  on  stucco,  than  by  linseed  or  nut  oil, 
boiled  with  driers  before  mentioned  —  taking  care,  in 
aU  cases,  not  to  lay  on  too  much,  so  as  to  render  the 
surface  rough  and  irregular,  and  not  more  than  the 
stucco  will  absorb.     It  should  then  be  covered  with 


three  or  four  coats  of  white  lead,  prepared  as  de- 
scribed for  painting  or  wainscoting,  allowing  each 
coat  sufficient  time  to  dry  hard.  If  time  will  permit, 
two  or  three  days  between  each  layer  will  be  advan- 
tageous. When  the  stucco  is  intended  to  be  finished 
in  any  given  tint,  as  gray,  light  green,  &e.,  it  wiU 
then  be  proper,  about  the  third  coat  of  painting,  to 
prepare  the  ground  for  such  a  tint,  by  a  slight  ad- 
vance towards  it.  Gray  is  made  with  white  lead, 
Prussian  blue,  ivory  black,  and  lake ;  sage  green,  pea, 
and  sea  greens,  with  white,  Prussian  blue,  and  fine 
yellows ;  apricot  and  peach,  with  lake,  white,  and 
Chinese  vermilion  ;  fine  yellow  fawn  color,  with 
burnt  terra  sienna,  or  umber  and  white ;  and  olive 
greens,  with  fine  Prussian  blues,  and  Oxfordshire 
ochre. 

Distemper,  or  painting  in  water  colors  mbced  with 
size  stucco  or  plaster,  which  is  intended  to  be  painted 
in  oU  when  finished,  but  not  being  sufficiently  dry  to 
receive  the  oil,  may  have  a  coating  in  water  colors, 
of  any  given  tint  required,  in  order  to  give  a  more 
finished  appearance  to  that  part  of  the  building. 
Straw  colors  may  be  made  with  French  whites  and 
ceruse,  or  white  lead  and  masticot,  or  Dutch  pink. 
Grays,  full,  with  some  whites  and  refiners'  verditer. 
An  inferior  gray  may  be  made  with  blue-black,  or 
bone  black,  and  indigo.  Pea  greens,  with  French 
green,  Olympian  green,  &c.  Fawn  color,  with  burnt 
terra  de  sienna,  or  burnt  umber  and  white,  and  so  of 
any  intermediate  tint.  The  colors  should  all  be 
ground  very  fine,  and  mixed  with  whiting  and  a  size 
made  with  parchment,  or  some  similar  substance. 
Less  than  two  coats  will  not  be  sufficient  to  cover 
the  plaster  and  bear  out  with  a  uniform  appearance. 
It  must  be  recollected,  that  when  the  stucco  is  suffi- 
ciently dry,  and  it  is  desurable  to  have  it  painted  in 
oil,  the  whole  of  the  water  colors  ought  to  be  re- 
moved, which  may  be  easily  done  by  washing,  and, 
when  quite  dry,  proceed  with  it  after  the  direction 
given  on  oil  painting  in  stucco. 

If  oil  plastering  has  become  disfigured  by  stains, 
or  other  blemishes,  and  if  it  be  desired  to  have  it 
painted  in  distemper,  it  is,  in  this  case,  advisable  to 
give  the  old  plastering,  when  properly  cleaned  off  and 
prepared,  one  coat,  at  least,  of  white  lead  ground  in 
oU,  and  used  with  spurits  of  turpentine,  which  will 
generally  fix  old  stains ;  and,  when  quite  dry,  take 
water  colors  very  readily. 


D.  H.  HILL  LIBRARY 

North  Carolina  State  College 


TABLES 


Slwwing  the  Weight  of  different  Materials,  Strength  of  Columns,  ^c,  ^c. 


OP  THE  COHESIVE  FORCE  OF  METALS  AND  WOODS. 

Weighl  or  Force  necessary  to  tear  asunder  one  Square  Inch,  in 
.Avoirdupois  Pounds. 


Copper,  cast 29-500 

"        wire 61-200 

Iron, cast;  gray, 2 fusion. 30-680 

"       «     English 52-000 

"       "     French 70-000 

«  "  "  soft...  63-600 
«       "      German 68-300 

Iron,  wrought 60-000 

«  "       Swedish...  72-000 

"  "       German . .  .69-000 


Ib9. 
Ash,  wliite,  seasoned 14-000 

"     red,  seasoned 17-800 

Birch 15-000 

Bay, 14-500 

Beech ,11-500 

Box 20-000 

Cedar 11-400 

Chestnut,  sweet 10-500 

Elm 13-400 

Fir,  strongest 12-000 

"    American 8-800 

Locust 20-500 


lbs. 

Iron,  wire 85-700-113- 

"     medium  bar 60-000 

«    inferior  bar 30-000 

Lead,  cast -880 

"      milled 3-320 

Silver  wire 38-257 

Steel,  soft 120-000 

"      fine 135-000 

"      razor,  tempered . .  150-000 


lbs. 

Mahogany 21-800 

"         Spanish 12-000 

Maple 10-500 

Oak,  American,  white. .  .11-500 

"    English 10-000 

"    seasoned 13-600 

Pine,  pitch 12-000 

"     Norway 13-000 

Sycamore 13-000 

Walnut 17-800 

Willow 13-000 


ON  THE   RESISTANCE   TO   CRUSHING   WOOD. 

According  to  the  experiments  of  Rondelet,  made  on  a  hydro- 
static press,  on  cubes  of  an  inch  in  lengUi,  it  required  from  5000 
to  6000  pounds  per  square  inch  to  crush  oak;  and  under  this 
pressure  its  length  was  diminished  more  than  one  third.  To  crush 
fir,  it  required  from  6000  to  7000  pounds  per  square  inch ;  and 
the  length  was  reduced  one  half.  Mr.  Rennes's  trials,  wliich  are 
considered  the  most  precise  on  this  subject,  afforded  results  con- 
siderably lower  than  those  of  Rondelet.  The  following  are  the 
results  of  liis  experiments :  — 

Base  1  inch  square,  height  1  inch,  Elm  was  crushed  by  1,284  lbs. 

"  "            "            "        "         White  deal       "  1,928 

"  "            "            "        "         American  pine  "  1,606 

"  "            "            "        «         English  oak      "  3,860 

"  "            "            '••        "         African  teak     "  8,480 

"  "            "        length  4  inches,     "        "        "  5,147 

'  3  inches  square,  length  6  to  9,     "       oak      "  60,480 

The  load  a  piece  of  timber  will  bear,  when  pressed  in  the  di- 
rection of  its  length,  without  risk  of  being  crushed,  may  be  found 


by  the  following  rule,  when  the  pressure  is  exactly  in  the  axis  of 

the  piece :  — 

Rule.  —  Multiply  the  area  of  the  piece  in  inches  by  the  weight 
that  has  been  found  capable  of  crushing  a  square  inch  of  the  same 
kind  of  wood.  (Sec  the  preceding  experiments.)  Then  one  fourth 
of  the  product  will  give  the  greatest  load  in  pounds  that  the  piece 
would  bear  with  safety. 

TO    SHOW  THE  WEIGHT  OR  PRESSURE 
A  Column  of  Cast  Iron  will  sustain  ivith  Safely. 


Length  or 

Heigbt  io 
feet. 

8 

10 

12 

14 

IC 

18 

20 

22 

24 

Weight 

Weight 

Weight 

Weight 

Weight 

Weight 

Weight 

Weight 

Weight 

in  cwts. 

in  cwts. 

in  cwts. 

in  cwts. 

in  cwts. 

in  cwts. 

in  cwts. 

in  cwts. 

in  cwta. 

24  in. 

91 

77 

65 

55 

47 

40 

34 

29 

25 

3     " 

145 

128 

111 

97 

84 

73 

64 

56 

49 

34  « 

214 

191 

172 

156 

135 

119 

106 

94 

a3 

4    " 

288 

266 

242 

220 

198 

178 

160 

144 

130 

44  " 

379 

354 

327 

301 

275 

251 

229 

208 

189 

5     " 

479 

452 

427 

394 

365 

337 

310 

285 

262 

6     " 

573 

550 

525 

497 

469 

440 

413 

386 

360 

7     « 

989 

959 

924 

887 

848 

808 

765 

725 

686 

8     " 

1289 

1259 

1224 

1185 

1142 

1097 

1052 

1005 

959 

9     " 

1672 

1640 

1603 

1561 

1515 

1467 

1416 

1364 

1311 

10     " 

2077 

2045 

2007 

1964 

1916 

1865 

1811 

17.55 

1697 

11     " 

2520 

2490 

2450 

2410 

2358 

2305 

2248 

2189 

2127 

12    " 

3020 

2970 

2930 

2900 

2830 

2780 

2730 

2670 

2600 

SHOWING  THE  WEIGHT 

Of  solid  Cylinders  of  Cast  Iron,  twelve  Indies  long,  in  .Avoirdupois 
Pounds. 


Inches 

Weipht 

Inches 

^Veifiht 

Inches 

Weight 

Inches 

Weight 

diam. 

in  lbs. 

diam. 

in  lbs. 

dinm. 

in  lbs. 

diam. 

in  lbs. 

1 

1-394 

24 

15-492 

44 

50-193 

8 

158-638 

i 

1-897 

2§ 

17-080 

4i 

55-926 

84 

179-087 

2-478 

21 

18-745 

5 

61-968 

9 

200-774 

ij 

3-137 

25 

20-488 

5.i 

68-319 

94 

223-704 

li 

3-873 

3 

22-308 

5i 

74-981 

10 

217-872 

13 

4-686 

31 

24-206 

53 

81-925 

104 

273-278 

14 

5-577 

3,i 

26-181 

6 

89-234 

11 

299-925 

IS 

6-545 

31 

28-234 

6.i 

96-825 

114 

327-811 

IJ 

7-591 

34 

30-364 

64 

104-726 

12 

356-935 

n 

8-714 

m 

.32-572 

m 

112-936 

13 

418-903 

2 

9-915 

m 

34-857 

7 

121-457 

14 

485-830 

2J 

11-193 

35 

37-219 

7.^ 

130-287 

15 

557-712 

2i 

12-548 

4 

39-660 

74 

139-428 

16 

634-552 

21 

13-981 

4i 

44-771 

7} 

148-878 

Note.  —  Cubic  inches  of  cast  iron  X  "263  =  lbs.  avoirdupois. 
Circular  inches  of  cast  iron  X  -2065  =  lbs.  avoirdupois. 


TABLES. 


169 


WEIGHT  OP  CAST-METAL  CYLINDERS. 

The  cylinders  are  solid,  each  one  foot  in  lengtli. 


Diameter. 

Iron  Cylinders. 

Copper  Cylinders. 

Brass  Cylinders. 

Lend  Cylinders. 

inch. 

lbs. 

Ills. 

lbs. 

U.S. 

1 

2-5 

3-0 

2-9 

3-9 

2 

9-8 

12-0 

11-4 

].->-5 

3 

22-1 

27-0 

25-8 

•M-8 

4 

39-3 

47-9 

45-8 

(11-9 

5 

Gl-4 

74-9 

71-(i 

90-7 

6 

88-4 

107-8 

103-0 

139-3 

7 

120-3 

14ti-8 

140-2 

189-f. 

8 

157-1 

191-7 

183-2 

347-7 

9 

198-8 

242-7 

231-8 

313-4 

10 

245-4 

299-5 

28G-2 

387-0 

WEIGHT  OF  CAST-IRON  PIPES. 

This  table  shoivs  the  weiirht  ot'  pipes  one  foot  long,  of  bores 
from  1  inch  to  1"2  inches  in  diameter,  advancinjr  by  one  fourth 
of  an  inch;  and  of  tiiickncsses  from  one  fourth  of  an  inch  to  one 
and  one  fourth  inch,  advancing  by  one  eighth  of  an  inch. 


Bore. 

K 

K 

U 

H 

« 

% 

1 

IH 

IH 

inch. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

1 

3-1 

5-1 

7-4 

10-0 

12-9 

16-1 

19-6 

23-5 

27-6 

u 

3-7 

6-0 

8-6 

11-5 

14-7 

18-3 

22-1 

26-2 

30-7 

1* 

4-3 

6-9 

9-8 

13-0 

16-6 

20-4 

24-5 

29-0 

.33-7 

li 

4-9 

7-8 

11-1 

14-6 

18-4 

22-6 

27-0 

31-8 

3G-8 

2 

5-5 

8-8 

12-3 

16-1 

20-3 

24-7 

29-5 

34-5 

39-9 

2* 

6-1 

9-7 

13-5 

17-6 

22-1 

26-8 

31-9 

37-3 

43-0 

24 

6-7 

10-6 

14-7 

19-2 

2:1-9 

28-9 

34-4 

40-0 

46-0 

2} 

7-4 

11-5 

10-0 

20-7 

25-7 

31-1 

36-8 

42-8 

491 

3 

8-0 

12-4 

17-2 

22-2 

27-6 

3:3-3 

39-3 

45-6 

52-2 

3* 

8-6 

12-3 

18-4 

23-8 

29-5 

35-4 

41-7 

48-3 

55-2 

Si. 

9-2 

14-2 

19-6 

25-3 

31-3 

37-6 

44-2 

511 

58-3 

3? 

9-8 

1.5-2 

20-9 

26-9 

33-1 

39-7 

46-6 

53-8 

61-4 

4 

10-4 

16-1 

22-1 

28-4 

35-0 

419 

49-1 

56-6 

64-4 

4i 

11-1 

17-1 

2;3-4 

.30-0 

36-9 

44-1 

51-6 

59-4 

G7-6 

44 

11-7 

18-0 

24-5 

31-4 

38-7 

46-2 

54  0 

62-1 

70-6 

4| 

12-3 

18-9 

25-8 

a3-o 

40-5 

48-3 

56-5 

64-9 

73-6 

5 

12-9 

19-8 

27-0 

34-5 

42-3 

50-5 

.58-9 

67-6 

76-7 

5* 

13-5 

20-7 

28-2 

36-1 

44-2 

52-6 

61-4 

70-4 

79-8 

54 

14-1 

21-G 

29-5 

37-6 

46-0 

54-8 

63-8 

73-2 

82-8 

53 

14-7 

22-G 

30-7 

39-] 

47-9 

56-9 

66-3 

76-0 

85-9 

6 

15-3 

23-5 

31-9 

40-7 

49-7 

59-1 

68-7 

78-7 

88-8 

6.1 

1(5-0 

24-4 

33-1 

42-2 

51-5 

61-2 

71-2 

81-2 

92-0 

64 

16-6 

25-3 

34-4 

43-7 

53-4 

63-4 

73-4 

84.2 

95-1 

6J 

17-2 

26-2 

35-6 

45-3 

55-2 

65-3 

76-1 

87-0 

98-2 

7 

17-8 

27-2 

36-8 

46-8 

56-8 

67-7 

78-5 

89-7 

101-2 

7| 

18-4 

28-1 

.38-1 

48-1 

58-9 

69-8 

81-0 

92-5 

104-2 

74 

19-0 

29-0 

39-1 

49-9 

60-7 

72-0 

83-5 

95-3 

107-4 

7? 

19-6 

29-7 

40-5 

51-4 

62-6 

741 

85-9 

98-0 

110-5 

8 

20-0 

30-8 

41-7 

52-9 

64-4 

76-2 

88-4 

100-8 

11:3-5 

8;J 

20-9 

31-7 

43-0 

54-5 

66-3 

78-4 

90-8 

103-5 

116-6 

84 

21-7 

32-9 

44-4 

56-2 

68-3 

80-8 

93-5 

106-5 

119-9 

8* 

22-1 

33-6 

45-4 

57-5 

70-0 

82-7 

95-7 

109-1 

122-7 

9 

22-7 

34-5 

46-6 

.59-1 

71-8 

84-8 

98-2 

111-8 

125-8 

9} 

23-3 

35-4 

47-9 

60-6 

73-6 

87-0 

100-6 

114-6 

128-9 

94 

2:^-9 

.36-4 

49-1 

62-1 

75-5 

89-1 

10:3-1 

117-4 

131-9 

m 

24-6 

37-3 

50-3 

63-7 

77-3 

91-3 

105-5 

120-1 

135-0 

10 

25-2 

38-2 

51-5 

65-2 

79-2 

93-4 

108-0 

122-8 

1:38-1 

10^ 

25-8 

39-1 

52-8 

66-7 

81-0 

95-6 

110-4 

125-6 

141-1 

104 

26-4 

40-0 

54-0 

68-3 

82-8 

97-7 

112-9 

128-4 

144-2 

lOJ 

27-0 

41-0 

55-2  !  69-8 

84-7 

99-9 

115-4 

131-2 

147-3 

n 

27-6 

41-9 

.56-5 

71-3 

86-5 

102-0 

117-8 

1.33-9 

1.50-3 

lU 

28-2 

42-8 

57-7 

72-9 

88-4 

104-2 

120-3 

i:3G-7 

153-4 

1U 

28-S 

43-7 

,58-9 

74-4    90-2 

106-3 

122-7 

139-4 

156-4 

111 

29-5 

44-6 

60-1 

75-9    920 

108-5 

125-2 

142-2 

159-5 

12 

30-1 

45-6 

61-4 

77-5    93-6 

110-6 

127  6 

145-0 

162-6 

22 


WEIGHT  OF  MET.VL   PLATES. 

This  table  shows  the  weight  of  a  square  foot  of  different  meta 
(dates,  of  thicknesses  from  one  si.\tcenth  of  an  inch  to  one  inch, 
advancing  by  a  sixteenth. 


Inch. 

Wrought 

Cast 

Cast 

Cast 

Cast 

Cast 

Cast 

Cast 

Iron. 

Iron. 

Copper. 

Brass. 

Lead. 

Zinc. 

Tin. 

Silver. 

IClbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

1 

2-5 

2-3 

2-9 

2-7 

3-7 

2-3 

2-4 

3-4 

2 

5-1 

4-7 

5-7 

5-5 

7-4 

4-7 

4-7 

6-8 

3 

7-6 

7-0 

8-G 

8-2 

11-1 

7-0 

71 

10-2 

4 

10-1 

9-4 

11-4 

11-0 

14-8 

9-4 

9-5 

13-6 

5 

12-7 

11-7 

14-3 

13-7 

18-5 

11-7 

11-9 

17-0 

6 

1.5-2 

14-0 

17-2 

16-4 

22-2 

14-0 

14-2 

20-5 

7 

17-9 

16-4 

20-0 

19-2 

25-9 

16-4 

16-6 

23-9 

8 

20-3 

18-8 

22-9 

21-9 

29-5 

18-7 

19-0 

27-:5 

9 

22-8 

21-1 

25-7 

24-6 

.^3-2 

21-1 

21-4 

30-7 

10 

25-4 

2.3-5 

28-G 

27-4 

36-9 

23-4 

23-7 

:34-l 

11 

27-9 

25-8 

31-4 

30-1 

40-G 

25-7 

26-1 

37-5 

12 

30-4 

28-1 

31-3 

32-9 

44-3 

28-1 

28-5 

40-9 

13 

32-9 

;50-5 

37-2 

35-6 

48-0 

30-4 

30-9 

44-3 

14 

35-5 

32-9 

40-0 

38-3 

51-7 

32-8 

33-2 

47-7 

15 

38-0 

35-2 

42-9 

41-2 

55-4 

3,5-1 

35G 

51-1 

16 

40-6 

37-6 

45-8 

43-9 

59-1 

37-5 

38-0 

54-6 

TIIE  WEIGHT,  IN  POUNDS,  OF  A  FOOT  IN  LENGTH  OF  CAST  IRON 


inch. 

i 

1* 
15 
14 

-3* 
II 

f 

? 
6i 


Square. 


•781 

1-756 

3125 

4-881 

7-031 

9-.56S 

12-.520 

1.5-818 

19-531 

23-e31 

28-12.5 

33-009| 

38-281 

43-943 

-50-000 

56-443 

63-281 

70-506: 

78-120I 

86-131: 

94-531 

103-318; 

112-.500I 

122058, 


Hexagon 


■bio 

1-528 

2-703 

4-225 

0  085 

8-281 

10-815 

13-990 

16-900 

20-450 

24-340 

28-565 

33-131 

38-031 

43-271' 

48-3531 

54-7681 

61-021 

67-5151 

74-549| 

81-815 

89-421 

97-368 

105-640 


Octagon. 

Circle. 

-65U 

-012 

1-471 

1-387 

2-603 

2-454 

4-065 

3-8-54 

5-8-56 

5-.521 

7-971 

7-515 

10412 

9-815 

iqiian-i  bquore. 
di-l 


13-lGS 
16-2.561 
19-6711 
23-412 
27-475 
31818 
3G-581 
41-621 
46-990 
52-681 
58-69(5 
65  040 
71-701 
78  696 
86-015 
93-656 
101-621 


12-42.5 
15-337 
18-559 
22-087 
25-921 
30-065 
31-512 
39-268 
44-331 
49-700 
55-375 
61-3.59 
67-709 
74-243 
81-r2G 
88  354 
95-871 


inch. 

64 

6J 

7 

7{ 

7.-1 

P 
8] 
84 

9^* 
% 

10 

104 
10.| 
lO^j 

u 

11} 
in 
11} 

12 


Hexagon 


031  114-271 
,231 
528 
■162 
037 
449 
099 


Octagon. 


125  219 

78l'201- 
031  214- 
968  257- 
500  270- 
318-281- 
.53l|'298- 
131,312- 
125,.327- 
216342- 
■281.357- 
023373 
■000  389^ 


087  177^ 
412187 
078!l99 
078  210- 
418  222- 
100  234^ 
105  247^ 
471,2fl0^ 
1.59  273^ 
193'286' 
.5.59;300- 
268,314- 
315329- 
693,344- 
32-5  3.59 
■475.374 


103-696 
Ul-82.5 
120-372 
128-986 
138-056 
147-415 
157-078 
167-049 
177-328 
187-912 
199-203 
600  210-800 
793,221-506 
3151233-318 
163,245-437 
341  257-8.59 
82s!270-593 
646  283-633 
796  296-978 


310-631 
324-587 
338-8.56 
353-428 


OF   TIIE  MT3IGHT   OF   A   CUBIC   FOOT   OF    VARIOUS   SUBSTANCES, 
In  common   Use  for  Building. 


lbs. 

Sand,  solid 112-5 

Sand,  loose 95 

Earth 93-75 

Common   Soil 124 

Strong  Soil 127 

Clay 120  to  1.35 

Clay  and  Stone 158 

Brick 119 

Granite 169 

Marble 166  to  169 

Sand,  one  cubic  yard 3037 

Common  Soil,  one  cubic  yard 3429 


170 


TABLES. 


THE  NIT.MDER  OP  NAILS  AND  SPIKES  TO  THE  POUND, 

Of  various  Sizes,  as  manufactured  at  the  Troy  Iron  and  .Vail  Fac- 
tory, JV.  Y. 


1 

Size  of 

Number 

Boat 

Diam. 

No.Spikes 

Sliip 

Diam. 

No.Spikes 

Nail9. 

to  the  lb. 

Spikes. 

of  Rod. 

to  the  lb. 

Spikes. 

of  Rod. 

to  the  lb. 

3  penny 

600 

No.  4 

i 

13 

No.  4 

A 

8 

4     " 

3G0 

"    5 

tV 

8 

"    5 

1 

6 

6     " 

200 

"    6 

i 

5 

"    6 

i 

5 

8     " 

110 

"    7 

i 

4 

"    7 

S 

3i 

10     " 

88 

"    8 

1 

3 

12     " 

68 

"    9 

T^if 

2 

20     « 

40 

"  10 

t\ 

14 

FOE   FINT)ING   THE  STRAIN  THAT  M.VY  BE  APPLIED   TO    A   HEMPEN 
ROPE   WITH  S.VFETY. 


Circum- 
ference. 

Pounds. 

Circum- 
ference. 

Pounds. 

Circum- 
ference. 

Pounds. 

Circum- 
ference. 

Pownds. 

1-00 

200-0 

3-00 

1800-0 

4-75 

4512-5 

6-50 

8450-0 

1-25 

312-5 

3-25 

2112-5 

5-00 

5000-0 

6-75 

9112-5 

1-50 

450-0 

3-50 

2450-0 

5-25 

5512-5 

7-00 

9800-0 

1-75 

612-5 

3-75 

2812-5 

5-50 

6050-0 

7-25 

10512-5 

2-00 

800-0 

4-00 

3200-0 

5-75 

6612-5 

7-50 

112.50-0 

2-25 

1012-5 

4-25 

3G12-5 

6-00 

7200-0 

7-75 

12012-5 

2-50 

1250-0 

4-50 

4050-0 

6-25 

7812-5 

8-00 

12800-0 

2-75 

1512-5 

WEIGHTS  OP  COPPER 

AND  SPIKES 

Size. 

Weight  of  1 

Cop'r  Bolts] 

per  foot. 

Number  of  Composition 
Spikes  to  tlio  100  lbs. 

Weipht  of  Sheatbing  Copper,  and 

Yellow  Sheatiiing  Metal, 

per  sheet. 

4 

i 

i 

1 

11 

li 

lbs. 

-7567 
1-18-24 
1-7027 
2-3176 
3-0270 
3-8312 
4-9298 

5  in.  round  head,  500 

5  "  square   "      434 
54"       "        "      400 

6  «       "        "     377 
64"       "        "     295 

7  "       "        "     275 
74"       "        "     210 

8  "       "        "     200 
84"       "        "      148 

Size. 

Weight. 

Size. 

Weight. 

ounces. 

14 
16 

18 
20 
22 

lbs.  ozs. 

4     1 

4  10 

5  4 

5  13 

6  7 

ounces. 

24 

26 
28 
30 
32 

lbs.  ozs. 

7     0 

7  9 

8  3 

8  12 

9  5 

WEIGHT  OF  LEAD  PIPES,  TWELVE  INCHES  LONG. 


SHOWING  THE  CONTENTS    OF   BRICK  WALLS,  NO.  OF  BRICKS,  &;c. 

This  table  is  calculated  in  round  numbers,  and  is  not  far  from 
the  average  of  waUs  made  of  the  Cliarlestown,  Fresh  Pond,  or 
eastern  bricks  —  the  latter  being  about  two  tlurds  tlie  size  of  the 
two  former. 


Width  of  Bricks 

Thickness 

No.  of  Bricks 

Contents  of 

to  a  superficial 

of  Wall,  in 

to  a  superlicial 

Willi,  in  su- 

foot. 

inches. 

foot. 

perlicial  feet. 

1000 

1 

4 

7 

143 

ii 

2 

8 

14 

71 

^^ 

3 

12 

21 

474 

t( 

4 

16 

28 

354 

(£ 

5 

20 

35 

28} 

(t 

6 

24 

42 

23} 

u 

7 

28 

49 

204 

(( 

8 

32 

56 

17} 

(I 

9 

36 

63 

15} 

1  cask  of  lime  will  plaster  about  50  yards. 
1  cask  will  skim  about  200  yards. 
4  casks  will  ordinarily  employ  45  bushels  of  sand. 
1  cask  will  ordinarily  employ  5  pecks  of  hair. 
00  yards  of  plastering  will  cover  1000  laths. 
100  pounds  of  tlireeponny  nails  will  lay  900  yards. 


§  in,  thick,  from  1  to  3  inches  bore. 

1  in.  thick,  from  1  to  3  inches  bore. 

s-ize. 

Weight 

Size. 

Weight  Size. 

Weight 

Size. 

Weight  Size. 

Weight  Size. 

Weight. 

1 

2-19 

li 

3-64 

24 

5-09 

1 

4-85 

1} 

7-76 

24 

10-66 

u 

2-43 

li 

3-8;j 

2S 

5-a3 

IJ 

5-34 

15 

8-17 

2g 

11-15 

li 

2-66 

2 

4-12 

2} 

5-57 

li 

5-81 

2 

8-73 

2} 

11-63 

15 

2-91 

2J 

4-29 

25 

5-82 

15 

6-3 

25 

9-21 

25 

12-12 

14 

3-15 

21 

4-61 

3 

6-06 

14 

6-79 

2i 

9-7 

3 

12-61 

11 

3-39 

21 

4-t)2 

lis 

7-27 

25 

10-25 

OF   CYLINDRIC.VL   ME.VSURES, 

Designed  for  the  computation  of  the  contents  of  lead  pipes,  from 
1  inch  diameter  to  3  and  upwards ;  also,  cisterns  of  10  feet  di- 
ameter and  under ;  and  the  quantity  and  weight  of  water  in 
pumps,  suction  pipes,  &c.,  of  1  inch  diameter  and  upwards. 


Indies 

(liaiuetcr. 

Cubic  feet 

and  decimal 

parts. 

Ale  gallons 
and  parts. 

Wine  gal- 
lons and 
parts. 

Weight  of 

water  in  lbs. 

and  parts. 

Dry  bushels 
and  parts. 

1 

•0055 

-033 

•04 

•34 

•0044 

2 

•0218 

-134 

•16 

1^36 

•0175 

3 

-0491 

•301 

■37 

3^06 

•0394 

4 

•0873 

■534 

-65 

5^45 

•0700 

5 

-136 

-835 

1-02 

8-.52 

•110 

d.     6 

-196 

1-20 

1-47 

12-'27 

•158 

g      7 

-207 

1-64 

2-00 

16-70 

•215 

■^      8 

-349 

2-14 

2-61 

21-82 

■281 

°      9 

-442 

2-71 

3-30 

27-61 

•355 

^    10 

•545 

3-34 

4-08 

34-09 

•438 

S   " 

•660 

4-04 

4-94 

41-25 

-530 

:^  12 

•785 

4-81 

5-88 

49-09 

•631 

^    24 

S    36 

3-14 

19-25 

23-52 

196-.36 

2-521 

7-07 

43-30 

52-92 

441-79 

5-68 

R    48 
■1    50 

12-57 

77-00 

94-08 

785-44 

10-10 

13-64 

83-55 

102-00 

852-21 

11-00 

W    60 

19-64 

l'20-30 

146-88 

1-227-19 

15-78 

72 

28-28 

173-20 

211-51 

17(i7-15 

22-72 

84 

38-49 

235-81 

287-88 

2405-28 

30-92 

96 

50-27 

308-00 

370-01 

3141-,59 

40-39 

108 

C):3-62 

389-79 

475-89 

397608 

51-12 

120 

78-54 

481-25 

587-.52 

4903-74 

63-11 

N.  B.  If  the  diameter  should  fall  between  any  of  the  numbers 
in  the  first  column,  the  mean  proportional  contents  may  be  found 
by  adding  the  two  contents  between  which  it  falls,  and  dividing 
by  2.  Suppose  it  falls  between  108  and  120  of  the  diameters,  re- 
quired the  wine  gallons  in  114  inches,  or  9  feet  6  inches  diameter, 
which  falls  between  587-52 

and  475-89 


2)106.3-41 


Answer,  531-704 

Or,  if  between  60  and  7"2,  say  64  inches,  or  5  feet  4  inches ;  one 
third  of  12  is  4  ;  tlien  required  the  cubic  feet  and  parts. 

28-28 
Subtract  19-64 


Divide 


Add 


3)8-64 

2-88 
19-64 


Answer,  22-52 

Any  depth  may  bo  found,  by  multiplying  by  the  depth  any  of 
the  numbers  in  the  contents;  as,  required  the  number  of  ale  gal- 
lons in  24  inches  diameter,  at  6  feet  deep. 

19-25 
6 


Answer, 


115-50 


GLOSSARY 


OF 


ARCHITECTURAL    TERMS 


Abacus  The  upper  member  of  the  capital  of  a  column  whereon  the 
architrave  rests.  Scammozzi  uses  this  term  for  a  concave  mouMing 
in  the  capital  of  the  Tuscan  pedestal,  whicli,  considering  its  etymol- 
ogy, is  an  error. 

Aedimest.     The  solid  part  of  a  pier,  from  which  an  arch  springs. 

Acanthus.  A  plant  called  in  English  hears  hrccch,  whose  leaves 
are  employed  for  decorating  the  Corinthian  and  Composite  capitals. 
The  leaves  of  the  acanthus  arc  used  on  the  bell  of  the  capital,  and 
distinguish  the  two  rich  orders  from  tlic  three  others. 

Accompaniments.  Buildings  or  ornaments  having  a  necessary  con- 
nection or  dependence,  and  which  serve  to  make  a  design  more  or 
less  complete  —  a  characteristic  pcculiai-ity  of  ornaments. 

AccouPLEMENT.  Among  carpenters,  a  tie  or  brace ;  sometimes  the 
entire  work,  when  framed. 

AcKOTEKiA.  The  small  pedestals  placed  on  the  extremities  and  apex 
of  a  pediment. 

Admeasukement.  Adjustment  of  proportions ;  technically,  an  esti- 
mate of  the  quantity  of  materials  and  labor  of  any  kind  used  in  a 
budding. 

Alcove.  The  original  and  strict  meaning  of  this  word,  which  is 
derived  from  the  Spanish  atcoba,  is  that  part  of  a  bed-chamber  in 
which  the  bed  stands,  and  is  separated  from  the  other  parts  of  the 
room  by  columns  or  pilasters. 

Amphiprostyle.  In  ancient  architecture,  a  temple  with  columns 
in  the  rear,  as  well  as  in  the  front. 

AiipniTnEATRE.  A  double  theatre,  of  an  elliptical  form,  on  the  ground 
plan,  for  the  exhibition  of  the  ancient  gladiatorial  tights  and  other 
shows. 

Ajtcones.  The  consoles  or  ornaments  cut  on  the  keys  of  arches, 
sometimes  serving  to  support  busts  or  other  figures. 

Annulet.  A  small,  square  moulding,  which  crowns  or  accompanies 
a  larger.  Also,  that  fillet  which  separates  the  flutings  of  a  column. 
It  is  sometimes  called  a  list,  or  listdla,  which  see. 

ANTiE.    A  name  given  to  pilasters  attached  to  a  wall. 

Apophyge.  That  part  of  a  column  between  the  upper  fillet  of  the 
base  and  the  cylindi-ical  part  of  the  shaft  of  the  column,  which 
is  usually  curved  into  it  by  a  cavetto. 

ABiEOSTYLE.  That  style  of  building  in  which  the  columns  are  dis- 
tant four,  and  sometimes  five,  diameters  from  each  other ;  but  the 
former  is  the  proportion  to  which  the  term  is  usually  applied.  This 
columnar  arrangement  is  suited  to  the  Tuscan  order  only. 

Akcade.  a  series  of  arches,  of  apertures,  or  recesses,  a  continued 
covered  vault,  or  arches  supported  on  piers  or  columns  instead  of 
galleries.  In  Italian  towns,  the  streets  are  lined  with  arcades  like 
those  of  Covcnt  Garden  and  the  Koyal  Exchange. 

Ancn.    An  artful   arrangement  of  bricks,  stones,  or  other  materials. 


in  a  curvilinear  form,  which,  by  their  mutual  pressure  and  support, 
perform  the  oflice  of  a  lintel,  and  can-y  superincumbent  weights  — 
the  whole  resting  at  its  extremities  upon  piers  or  abutments. 

Arch  Bcttress,  or  Flying  Buttress,  (in  Gothic  architecture,)  an 
arch  springing  from  a  buttress  or  pier,  and  abutting  against  a  wall. 

Archeion.  The  most  retired  and  secret  place  in  Grecian  temples, 
used  as  a  treasuiy,  wherein  were  depo.<itcd  the  richest  treasures 
pertaining  to  the  deity  to  whom  tlio  temple  was  dedicated. 

Architect.  One  who  designs  and  superintends  the  erection  of 
buildings. 

Architrave.  The  lower  of  the  primary  divisions  of  the  entabla- 
ture.   It  is  placed  immediately  upon  the  abacus  of  the  capital. 

Astragal.  From  the  Greek  word  for  a  bone  in  the  foot,  to  which 
this  moulding  was  supposed  to  bear  a  resemblance.  A  small 
moulding,  whose  profile  is  semicircular,  and  which  bears  also  the 
name  of  talon,  or  tondino.  The  astragal  is  often  cut  into  beads 
and  berries,  and  used  in  ornamental  entablatures  to  separate  the 
faces  of  the  architrave. 

Attic.  A  tenn  that  expresses  any  thing  invented  or  much  used  in 
Attica,  or  the  city  of  Athens.  A  low  story  erected  over  an  order 
of  architecture,  to  finish  the  upper  part  of  the  building,  being  chiefly 
used  to  conceal  the  roof,  and  give  greater  dignity  to  the  design. 

Attic  Base.    See  Base. 

Attic  Order.  An  order  of  low  pilasters,  generally  placed  over  some 
other  order  of  columns.  It  is  improperly  so  called,  for  the  aiTange- 
ment  can  scarcely  be  called  an  order. 

AuRiEL,  or  Oriel,  (in  Gothic  architecture,)  a  window  projecting  out- 
wards for  private  conference  ;  whence  its  appellation. 

Balcony.  A  projection  from  the  siu-face  of  a  wall,  supported  by 
consoles  or  pillars,  and  surrounded  by  a  balustrade. 

Baluster.  A  small  pillar  or  pilaster,  serving  to  support  a  rail.  Its 
form  is  of  considerable  variety,  in  difltrent  examples.  Sometimes  it 
is  round  ;  at  other  times  square :  it  is  adorned  with  mouldings  and 
other  decorations,  according  to  the  richness  of  the  order  it  accom- 
panies. 

Balustrade.  A  connected  range  of  a  number  of  balusters  on  bal- 
conies, terraces  around  altars,  &c.     See  Baluster. 

Band.  A  term  used  to  express  what  is  generally  called  a  face  or 
facia.  It  more  properly  means  a  flat,  low,  square,  profiled  member, 
without  respect  to  its  place.  That  from  which  the  Corinthian  or 
other  raodillions  or  the  dentils  project  is  called  the  modilUon  band, 
or  the  dentil  band,  as  the  case  may  be. 

Bandelet.  A  .liminutive  of  the  foregoing  term,  used  to  express  any 
narrow,  flat  moulding.  The  ta;nia  on  the  Doric  architrave  is  called 
its  bandelet. 


172 


GLOSSARY    OF    ARCHITECTURAL    TERMS. 


Baxkek.    a  stone  bench,  on  which  masons  cut  and  square  their  work. 
Banquet.    The  footway  of  a  bridge  raised  above  the  carriage-way. 
Babrel  Drain.    A  drain  of  the  form  of  a  Iiollow  cylinder. 
Base.    The  lower  part  of  a  column,  moulded  or  plain,  on  which  the 

shaft  is  placed. 
Basement.    The  lower  part  or  story  of  a  building,  on  which  an 
order  is  placed,   with  a  base  or  plinth,  die,  and  cornice. 

Basil.  A  word  used  by  carpenters,  &c.,  to  denote  the  angle  to  which 
any  edge  tool  is  ground  and  fitted  for  cutting  wood,  &c. 

Basin,  en  Coquille,  that  is,  shaped  like  a  shell. 

Basin  is  likewise  used  for  a  dock. 

Basket.  A  kind  of  vase  in  tho  form  of  a  basket,  Blled  with  flowers 
or  fruits,  seri'ing  to  terminate  some  decoration. 

Basilica.  A  town  or  court  hall,  a  cathedral,  a  palace,  where  kings 
administer  justice. 

Basso  Eilieto,  or  Bas  Relief.  The  representation  of  figures  pro- 
jecting from  a  background,  without  being  detached  from  it.  Though 
this  word,  in  general  language,  implies  all  kinds  of  rilievoes,  from 
that  of  coins  to  more  than  one  half  of  the  thickness  from  the  back- 
ground. 

Bath.  A  receptacle  of  water,  appropriated  for  the  purpose  of 
bathing. 

Batten.  A  scantling  of  stuff  from  two  to  six  inches  broad,  and 
from  §  to  two  inches  thick,  used  in  the  boai'ding  of  floors  ;  also  upon 
walls,  in  order  to  secure  the  lath  on  which  the  plaster  is  laid. 

Batter.  'When  a  wall  is  built  in  a  direction  that  is  not  per- 
pendicular. 

Battlements.  Indentations  on  the  top  of  a  parapet,  or  wall,  first 
used  in  ancient  fortifications,  and  afterwards  applied  to  churches 
and  other  buildings. 

Bat,  (in  Gothic  architectm'c,)  an  opening  between  piers,  beams,  or 
muUions. 

Bat  Window.    See  Auriel. 

Bead  and  Flusu  Work.  A  piece  of  panel  work,  with  a  bead  ran  on 
each  edge  of  the  included  panel. 

Bead  and  But  Work.  A  piece  of  framing  in  which  the  panels  are 
flush,  having  beads  stuck  or  run  upon  the  two  edges  witU  the  grain 
of  the  wood  in  their  direction. 

Bed  Mouldings.  Those  mouldings  in  all  the  orders  between  the 
corona  and  frieze. 

Billet  Moulding,  (in  Gothic  architecture,)  a  cylindrical  moulding, 
discontinued  and  renewed  at  regular  intervals. 

Boltel,  (in  Gothic  architecture,)  slender  shafts,  whether  an-anged 
round  a  pier,  or  attached  to  doors,  windows,  &c.  The  term  is  also 
used  for  any  cylindrical  moulding. 

Boss,  (in  Gothic  architecture,)  a  sculptured  protuberance  at  the  inter- 
jnnction  of  the  ribs  in  a  vaulted  roof. 

Bossage.  (A  French  term.)  Any  projection  left  rough  on  the  face 
of  a  stone  for  the  purpose  of  sculpture,  which  is  usually  the  last 
thing  finished. 

BouLTiN.  A  name  given  to  the  moulding,  called  the  egg  or  quarter 
round. 

Broach,  (in  Gothic  architecture,)  a  spire,  or  polygonal  pjTamid, 
whether  of  stone  or  timber. 

Bracket,  (in  Gothic  ai'chitceture,)  a  projection  to  sustain  a  statue,  or 
other  ornament,  and  sometimes  supporting  the  ribs  of  a  roof 

Bulk.  A  piece  of  timber  from  four  to  ten  inches  square,  and  is  some- 
times called  ranging  timber. 

Buttress,  fi"  Gotliic  architecture,)  a  projection  on  the  exterior  of  a 
wall,  to  strengtheii  the  piers  and  resist  the  pressure  of  the  arches 
within. 

Cabling.    The  filling  up  of  the  lower  part  of  the  fluting  of  a  column 


with  a  solid  cylindrical  piece.    Flutings  thus  treated  are  said  to  be 

cabled. 
Caisson.    A  name  given  to  the  sunk  panels  of  various  geometrical 
forms,  symmetrically  disposed  in  flat  or  vaulted  ceilings,  or  in  sofiits, 
generally. 
Canopt,  (in  Gothic  architecture.)  the  ornamented  dripstone  of  an  arch. 

It  is  usually  of  the  ogee  form. 
Canted,  (in  Gothic  architecture,)  any  part  of  a  building  having  its 

angles  cut  off  is  said  to  be  canted. 
Capital.     The  head  or  uppermost  part  of  a  column  or  pilaster. 
Carpenter.    An  artificer  whose  business  is  to  cut,  fasliion,  and  join 
timbers  together,  and  other  wood,  for  the  purjjose  of  building :  the 
word  is  from  the  French  charpcnlicr,  derived  from  charpentie,  which 
signifies  timber. 
Carpentry,  or  that  branch  which  is  to  claim  our  attention,  is  divided 
into  three  principal  heads,  viz..  Constructive,  Descriptive,  and  Me- 
chanical ;  of  these,  Descriptive  carpentry  shows  the  lines  or  methods 
for  forming  every  species  of  work  in  piano,  by  tho  rules  of  geometry  j 
Constructive  carpentry,  the  practice  of  reducing  the  wood  into  par- 
ticular foi-ms,  and  joining  the  forms  so  produced,  so  as  to  make  a 
complete  whole,  according  to  the  intention  of  the  design ;  and  Me- 
chanical carpentry  displays  the  relative  strength  of  the  timbers,  and 
the  strains  to  which  tliey  arc  subjected  by  their  disposition. 
Cartoucd.    Tlic  same  as  raodillions,  except  tliat  it  is  exclusively  used 
to  signify  those  blocks  or  modillions  at  the  caves  of  a  house.    See 
Modillion, 
Caryatides.    Figures  of  women,  which  serve  instead  of  columns  to 

support  the  entablature. 
Casement.    The  same  as  Scotia,  which  see.     The  term  is  also  used 

for  a  sash  hung  upon  hinges. 
Cauliculus.    The  volute  or  twist  under  the  flower,  in  the  Corinthian 

capital. 
Cavetto.    a  hollow  moulding,  whose  profile  is  a  quadrant  of  a  circle, 

principally  used  in  cornices. 
Cell.     Sec  Naos. 

Cincture.    A  ring,  list,  or  fillet,  at  the  top  or  bottom  of  a  column, 

serving  to  divide  the  shaft  of  the  column  from  its  cajiital  and  base. 

Chamfer,   (in   Gothic  architecture,)   an  arch,  or  jamb  of  a  door, 

canted. 
Cdamp,  (in  Gothic   architecture,)  a  flat  surface  in  a  wall  or  pier,  as 

distinguished  from  a  moulding,  shaft,  or  panel. 
CiNQUEFOiL,  (in  Gothic  architecture,)  an  ornamental  figure,  with  five 

leaves  or  points. 
Column.     A  member  in  architecture  of  a  cylindrical  form,  consisting 
of  a  base,  a  shaft  or  body,  and  a  capital.    It  ditfors  from  the  pilaster, 
which  is  square  on  the  plan.     Columns  should  always  stand  per- 
pendicularly. 
Composite  Order.    One  of  the  orders  of  ai'chitecture. 
Cope,  Coping,  (in  Gothic  architecture.)  the  stone  covering  the  top  of 

a  wall  or  parapet. 
CoRREL,  (in  Gothic  architecture,)  a  kind  of  bracket.    The  term  is 
generally  used  for  a  continued  series  of  brackets  on  tho  exterior  of 
a  building  supporting  a  projecting  battlement,  which  is  called  a 
corbel  table. 
CoKiNiniAN  Order.    One  of  the  orders  of  architecture. 
Cornice.    The    projection,   consisting    of  several  mcmbci-s,  which 
crowns  or  finishes  an  entablature,  or  tho  body  or  part   to  which 
it  is  annexed.    The  cornice  used  on  a  pedestal  is  called  the  cap  of 
the  pedestal. 
Corona,  is  that  flat,  square,  and  massy  member  of  a  cornice,  more 
usually  called  the  drip  or  larmier,  whose  situation  is   between  the 
cimatium  above  and  the  bed  moulding  below.     Its  use  is   to  caiTV 
the  water,  drop  by  drop,  from  the  building. 


GLOSSARY  OF  ARCHITECTURAL  TERMS. 


173 


Corridor.  A  gallery  ov  o])Cn  communication  to  the  diffoi-cnt  apart- 
ments of  a  house. 

COKSA.  The  name  given  by  Vitruvius  to  a  platbancl  or  square  facia, 
whose  height  is  more  tlian  its  i)rojcctiiro. 

Crenelle,  (in  Gothic  architecture.)  tlie  opening  of  an  embattled 
parapet. 

Crest,  (in  Gothic  architecture,)  a  crowning  ornament  of  leaves  run- 
ning on  the  top  of  a  screen  or  other  ornamental  work. 

Crocket,  (in  Gothic  architecture,)  an  ornament  of  leaves,  running  up 
the  sides  of  a  gable,  or  ornamented  canopy. 

CcPOLA.  A  small  room,  either  circular  or  polygonal,  standing  on  the 
top  of  a  clonic.    By  some  it  is  called  a  lantern. 

CnsuioxED.     See  Frieze. 

Cusp,  (in  Gothic  architecture.)  a  name  for  the  segments  of  cutIcs 
forming  the   trefoil,  quatrcfoil,  &c. 

Ctma,  called  also  Ci/malium,  its  name  arising  from  its  resemblance  to 
a  wave.  A  moulding  which  is  hollow  in  its  upper  part,  and  swelling 
below. 

Decagon.    A  plain  figure,  having  ten  sides  and  angles. 

Decastyle.    A  building  having  ten  columns  in  front. 

Decejipeda.  (Decern,  ten,  and  pes,  foot,  Lat.)  A  rod  of  ten  feet, 
used  by  the  ancients  in  measuring.  It  was  subdivided  into  twelve 
inches  in  each  foot,  and  ten  digits  in  each  inch ;  like  surveyors'  rods 
used  in  measuring  short  distances,  &c. 

Decimal  Scale.  Scales  of  this  kind  are  used  by  draughtsmen,  to 
regulate  the  dimensions  of   their  drawings. 

Decoration.  Any  thing  that  enriches  or  gives  beauty  and  ornament 
to  the  orders  of  architecture. 

Demi  Metope.  The  half  a  metope,  which  is  found  at  the  retiring  or 
projecting  angles  of  a  Doric  frieze. 

Dentils.  Small,  square  blocks  or  projections  used  in  the  bed  mould- 
ings of  the  cornices  in  the  Ionic,  Corinthian,  Composite,  and  some- 
times Doric  orders. 

Details  of  an  Edifice.  Drawings  or  delineations  for  the  use  of 
builders,  othenvise  called  working  plans. 

Diagonal  Scale  is  a  scale  subdivided  into  smaller  parts  by  second- 
ary intersections  or  oblique  lines. 

Diameter.  The  line  in  a  circle  passing  from  the  circumference 
through  the  centi'e. 

Diamond.  A  sharp  instrument  formed  of  that  precious  stone,  and 
used  for  cutting  glass. 

Diapered,  (in  Gothic  architecture,)  a  panel,  or  other  flat  surface, 
sculptured  with  flowers,  is  said  to  be  diapered. 

Diasttle.  That  intercolumniation  or  space  between  columns,  con- 
sisting of  three  diameters  —  some  say  fom-  diameters. 

Die,  or  Dte.  A  naked,  square  cube.  Thus  the  body  of  a  pedestal, 
or  that  part  between  its  base  and  cap,  is  called  the  die  of  the  pedes- 
tal.    Some  call  the  abacus  the  die  of  the  capital. 

Dimension.  (D/mrf/er,  Lat.)  In  geometry,  is  either  length,  breadth, 
or  thickness. 

Diminution.  A  term  expressing  the  gradual  decrease  of  thickness 
in  the  upper  part  of  a  column. 

Dipteral.  A  term  used  by  the  ancients  to  express  a  temple  with  a 
double  range  of  columns  in  each  of  its  flanks. 

Dodecagon.  A  regular  polygon,  with  twelve  equal  sides  and 
angles. 

DoDECASTVLE.    A  building  having  twelve  columns  in  front. 

Dome.  An  arched  or  vaulted  roof,  springing  from  a  polygonal,  circu- 
lar, or  elliptic  plane. 

Doric  Order.    One  of  the  five  orders  of  architecture. 

Dormant,  or  Dormer  Window,  (in  Gothic  architecture,)  a  window 
set  upon  the  slope  of  a  roof  or  spire. 


DooKS.  Flat  pieces  of  wood,  of  the  shape  and  size  of  a  brick,  in- 
serted in  brick  walls,  sometimes  called  plugs  or  wooden  bricks. 

Door.  The  gate  or  entrance  of  a  house,  or  other  building,  or  of  an 
apartment  in  a  house. 

Dormitory.    A  sleeping-room. 

Drawing,  or  Witiidrawino-uoom.  A  lai-ge  and  elegant  apart- 
ment, into  which  the  company  witlidraw  after  dinner. 

Dressing-room.  An  apartment  contiguous  to  the  sleeping-room, 
for  the  convenience  of  dressing. 

Drip,  in  (Gothic  architectm-e,)  a  moulding  much  resembling  the  ci- 
matium  of  Roman  architecture,  and  used  for  the  same  purpose  as  a 
canopy  over  the  arch  of  a  door  or  window. 

Drops.    Sec  GiUkc. 

EcniNUS.  The  same  as  the  ovolo  or  quarter  round  ;  but  perhaps  it  is 
only  called  echinus  with  propriety. 

Edging.  The  reducing  the  edges  of  ribs  or  rafters,  that  they  may 
range  together. 

Elbows  of  a  Window.  The  two  panelled  flanks,  one  under  each 
shutter. 

Elevation.  A  geometrical  projection  drawn  on  a  plane,  perpendic- 
ular to  the  horizon. 

Embankments  arc  artificial  mounds  of  earth,  stone,  or  other  materi- 
als, made  to  confine  rivers,  canals,  and  reseiwou-s  of  water  within 
their  prescribed  limits ;   also  for  levelling  up  of  railroads,  &c. 

Embrasure,  (in  Gothic  arcliitccture,)  the  same  as  Crenelle,  which  sec. 

Encaepcs.  The  festoons  on  a  frieze,  consisting  of  fruits,  flowers,  and 
leaves.    See  Festoon. 

Entablature.  The  assemblage  of  parts  supported  by  the  column. 
It  consists  of  three  parts  —  the  architrave,  frieze,  and  cornice. 

Entail,  (in  Gothic  architecture,)  delicate  carving. 

Entasis.  The  slight  curvature  of  the  shafts  of  ancient  Grecian  col- 
umns, particularly  the  Doric,  which  is  scai'cely  perceptible,  and 
beautifully  graceful. 

Entresol.     See  Mezzanine. 

Epistylum.    The  same  as  Architrave,  which  see. 

EusTYLE.  That  intercolumniation  which,  as  its  name  would  import, 
the  ancients  considered  the  most  elegant,  namely,  two  diameters 
and  a  quai-ter  of  a  column.  Vitravius  says  this  manner  of  arran- 
ging columns  exceeds  all  others  in  sti'ength,  convenience,  and  beauty. 

Facade.  The  fi\ce  or  front  of  any  considerable  building  to  a  street, 
court,  garden,  or  other  place. 

Facia.  A  flat  member  in  the  entablature  or  elsewhere,  being  in  fact 
nothing  more  than  a  band  or  broad  fillet. 

Fane,  Phane,  Vane,  (in  Gothic  architecture,)  a  plate  of  metal  usu- 
ally cut  into  some  fantastic  form,  and  turning  on  a  pivot,  to  deter- 
mine the  course  of  the  wind. 

Fastigium.     See  Pediment. 

Feather-edged  Boards  are  narrow  boards,  made  thin  on  one 
edge.     They  are  used  for  the  facings  or  boai-ding  of  wooden  walls. 

Festoon.  An  ornament  of  carved  work,  representing  a  wreath  or 
garland  of  flowers  or  leaves,  or  both,  interwoven  with  each  other. 

Fillet.  The  small,  square  member  which  is  placed  above  or  below 
the  various  square  or  curved  members  in  an  order. 

FiNiAL,  (in  Gothic  architecture,)  the  ornament,  consisting  usually  of 
four  crockets,  which  is  employed  to  finish  a  pinnacle,  gable,  or 
canopy. 

Flank.  The  least  side  of  a  pavilion,  by  which  it  is  joined  to  the 
main  building. 

Flatnino,  in  inside  house  painting,  is  the  mode  of  finishing  without 
leaving  a  gloss  on  the  surface,  which  is  done  by  adding  the  spirits 
of  turpentine  to  unboiled  linseed  oil. 


174 


GLOSSARY  OF  ARCHITECTURAL  TERMS. 


Flieks  are  steps  in  a  series  which  are  parallel  to  each  other. 

Fligut  of  Staies  is  a  series  of  steps,  from  one  landing-place  to 
another. 

Floors.    The  bottom  of  rooms. 

Flutings.  The  vertical  channels  on  the  shafts  of  columns,  ■which 
are  usually  rounded  at  the  top  and  bottom. 

Folding  Docks  arc  made  to  meet  each  other  from  opposite  jambs, 
on  which  they  are  hung. 

Foliage.  An  ornamental  distribution  of  leaves  or  flowers  on  various 
parts  of  the  building. 

FoREsnoKTEX.  A  term  applicable  to  the  drawings  or  designs  in 
which,  from  the  obliquity  of  the  \iew,  the  object  is  represented  as 
receding  from  the  opposite  side  of  the  plane  of  the  projection. 

FonNDATiON.  That  part  of  a  building  or  wall  which  is  below  the 
surface  of  the  ground. 

Foot.    A  measure  of  twelve  inches,  each  inch  being  three  barleycorns. 

Fbame.  The  name  given  to  the  wood  work  of  windows  enclosing 
glass,  and  the-  outward  work  of  doors  or  windows,  or  window  shut- 
ters, enclosing  panels ;  and  in  carpentry,  to  the  timber  work  sup- 
porting floors,  roofs,  ceilings,  or  to  the  intersecting  pieces  of  timbers 
forming  partitions. 

Feet.  A  kind  of  ornamental  work,  which  is  laid  on  a  plane  surface. 
The  Greek  fret  is  formed  by  a  series  of  right  angles  of  fiUcts,  of 
various  forms  and  figures. 

Fkieze,  or  Frize.  The  middle  member  of  the  entablature  of  an 
order,  which  separates  the  architrave  and  the  cornice. 

Frontispiece.  The  face  or  fore  front  of  a  house;  but  it  is  a  term 
more  usually  applied  to  its  decorated  entrance. 

Front.    A  name  given  to  the  principal  interior  facade  of  a  building. 

Frustum.  A  piece  cut  oft'  from  a  regular  figure ;  the  frustum  of  a 
cone  is  the  part  that  remains  when  the  top  is  cut  oft'  by  an  intersec- 
tion parallel  to  its  base,  as  the  Grecian  Doric  column  without  a  base. 

FuRRiNGS  are  flat  pieces  of  timber,  plank,  or  board,  used  by  carpen- 
ters to  bring  dislocated  work  to  a  regular  surface. 

FcST.    The  shaft  of  a  column.     See  Shaft. 

Gable,  (in  Gothic  architecture,)  the  triangularly-headed  wall  which 
covers  the  end  of  a  roof. 

Gable  Window,  (in  Gothic  architecture,)  a  window  in  a  gable. 
These  are  generally  the  largest  windows  in  the  composition,  fre- 
quently occupying  nearly  the  whole  space  of  the  wall. 

Gablet,  (in  Gothic  architecture,)  a  little  gable.     See  Canopij. 

Gage.  In  carpentry,  an  instrument  to  strike  a  line  parallel  to  the 
straight  side  of  any  board  or  piece  of  stuft". 

Gain.     The  bevelled  shoulder  of  a  binding  joist. 

Garland,  (in  Gothic  architecture,)  an  ornamental  blind  surrounding 
the  top  of  a  tower  or  spire. 

Glyphs.  The  vertical  channels  sunk  in  the  triglyphs  of  the  Doric 
frieze. 

GoLA,  or  GuLA.    The  same  as  Ogee,  which  see. 

Gorge.    The  same  as  Cavcilo,  which  see. 

Gouge.    A  chisel  of  a  semicircular  form. 

Granite.  A  genus  of  stone  much  used  in  building,  composed  chiefly 
of  quartz,  feldspar,  and  mica,  forming  rough  and  large  masses  of 
very  great  hardness. 

Groin,  (in  Gothic  architecture,)  the  diagonal  line  formed  by  the  inter- 
section of  two  vaults  in  a  roof. 

Groined  Ceiling.  A  surface  formed  of  three  or  more  curved  sur- 
faces, so  that  every  two  may  form  a  groin,  all  the  groins  terminating 
at  one  extremity  in  a  common  point. 

Groove,  or  Mortise.  The  channel  made  by  a  joiner's  pUne  in  the 
edge  of  a  moulding,  style,  or  rail,  to  receive  the  tenon. 

Gbound  Floor.    The  lowest  story  of  a  building. 


Ground  Plane.    A  line  forming  the  ground  of  a  design  or  picture, 

which  line  is  a  tangent  to  the  surface  of  the  face  of  the  globe. 
Ground  Plot.    The  ground  on  which  a  building  is  placed. 
Grounds.    Joiners  give  this  name  to  narrow  strips  of  wood  put  in 

walls  to  receive  the  laths  and  plastering. 
GuTT^,  or  Drops.    Those  frusta  of  cones  in  the  Doric  entablature 

which  occur  in  the  arcliitrave  below  the  ttenia  under  each  triglyph. 
Gutters  are  a  kind  of  canals  iu  the  roofs  of  houses,  to  receive  and 

carry  off  rain  water. 

Halving.    The  jtmction  of  two  pieces  of  timber,  by  inserting  one  into 

the  other;  in  some  cases,  to  be  preferred  to  mortising. 
Hand  Railing.     The  art  of  forming  liand  rails  round  circular  and 

elliptic  well  holes  without  the  use  of  the  cylinder. 
H-iNGiNG  Style  of  a  Door  is  that  to  which  the  hinges  are  fixed. 
Heel  of  a  Rafter.    The  end  or  foot  that  rests  upon  the  wall  plate. 
Helical  Line  op  a  Hand  Rail.    The  line,  or  spii-al  line,  represent- 
ing the  form  of  the  hand  rail  before  it  is  moulded. 
Helix.    The  curling  stalk  under  the  flower  iu  the  Corinthian  capital. 

See  Caulicuhis. 
Hem.    The  spiral  projecting  part  of  the  Ionic  cupital. 
Hexastyle.    a  building  having  six  columns  in  front. 
Hood  Mould,  (in  Gothic  architecture.)     See  Drip. 
Hook  Pins.     The  same  as  draio  bore  pins,  to  keep  the  tenons  in  their 

place,  while  in  the  progress  of  framing ;  the  pin  has  a  head  or  notch 

in  the  outer  end,  to  draw  it  at  pleasure. 
Hyp.ethral.     Open  at  top ;  uncovered  by  a  roof. 
HvPERTnYROx.     The  lintel  of  a  doorway. 
HvpoTRACnELiUM.    A  term  given  by  Vitruvius  to  the  slenderest  part 

of  the  shaft  of  a  column,  where  it  joins  the  capital.    It  signifies  the 

part  under  the  neck. 

Inciinooraph  Y.  The  transverse  section  of  a  building,  which  represents 
the  circumference  of  the  whole  edifice ;  the  ditfcrcnt  rooms  and 
apartments,  with  the  thickness  of  the  walls  ;  the  dimensions  and  sit- 
uation of  the  doors,  windows,  chimneys  ;  the  projection  of  columns, 
and  every  thing  that  could  be  seen  in  such  a  section,  if  rcilly  made 
in  a  building. 

Impost.  The  layer  of  stone  or  wood  that  crowns  a  door  post  or  pier, 
and  which  supports  the  base  line  of  an  arch  or  arcade ;  it  generally 
projects,  iind  is  sometimes  formed  of  an  assemblage  of  mouldings. 

Inch.  The  twelfth  part  of  a  foot.  For  tlie  purpose  of  reckoning  in 
decimal  fractions,  it  is  divided  into  ten  parts  or  integers. 

Inclined  Plane.  One  of  the  mechanical  powers  used  for  raising 
ponderous  bodies,  in  many  instances,  of  immense  weight ;  a  declivity 
of  a  hill,  &c. 

Insular  Column  is  a  column  standing  by  itself. 

Insulated.    Detached  from  another  building. 

Intaglio.    Any  thing  with  figures  in  relief  on  it. 

Intercolumnhtion.     The  distance  between  two  columns. 

Intrados.     The  undcr-cuned  surface  or  soflit  of  an  arch. 

Inverted  Arches.  Such  as  have  their  intrados  below  the  centre  or 
axis. 

Ionic  Order.     One  of  the  orders  of  arohitcctm-c. 

Jack  Plane.  A  plane  about  eighteen  inches  long,  to  prepare  for  the 
trying  plane. 

Jack  Rafters.  The  jack  timbers,  which  arc  fastened  to  the  hip  raft- 
ers and  the  wall  plates. 

Jambs.  The  side  pieces  of  any  opening  in  a  w.ill,  which  bear  the  piece 
that  discharges  the  superincumbent  weight  of  such  wall. 

Joinery,  in  building,  is  confined  to  the  nicer  and  more  ornamental 
parts. 


GLOSSARY  OF  ARCHITECTURAL  TERMS. 


stuff  for  joints, 


Jointer.    A  tool  used  for  straightening  and  preparing  stud 
&c.     Tliis  jointer  is  about  two  feet  eight  or  ten  inches  Ion 

Kerk.     Tlio  slit  or  cut  in  a  piece  of  timber,  or  in  a  stone,  by  a  saw. 
Kjng  Post.     The  middle  post  in  a  section  of  rafters. 

LABEt,  (in  Gothic  architecture.)  a  name  for  the  drip  or  liood  moulding 
of  an  arch  when  it  is  returned  square. 

LACtrxAE,  or  Laqueae.    The  same  as  Soffit. 

Laxtekjj,  (in  Gothic  architecture,)  a  turret  or  tower  placed  above  a 
building,  pierced  either  with  windows  to  admit  light,  or  liolcs  to  lot 
out  steam. 

LARMiEn.    Called  also  Corona,  which  see. 

Lath.  A  naiTow  slip  of  wood,  1}  to  \h  inclics  wide,  4  to  3  inch  thick, 
and  fom-  feet  long,  used  in  plastering. 

Leaves.  Ornaments  representing  natural  leaves.  The  ancients  used 
two  sorts  of  leaves,  natural  and  imaginary.  The  natural  were  those 
of  the  laurel,  palm,  acanthus,  and  olive;  but  they  took  such  liberties 
in  the  form  of  these,  that  they  might  almost  bo  said  to  be  imagi- 
nary, too. 

Level.    A  surface  which  inclines  to  neither  side. 

Lining.  Covering  for  the  interior,  as  casing  is  covering  for  the  exte- 
rior surface  of  a  building. 

Lintel.  A  piece  of  timber  or  stone,  placed  horizontally  over  a  door, 
■window,  or  other  opening. 

List,  or  Listel.    The  same  as  fillet  or  annulet. 

Listing.    The  catting  the  sapwood  out  from  both  edges  of  a  board. 

Loop,  (in  Gothic  architectui'C,)  a  small,  narrow  window. 

Louvre,  (in  Gothic  architecture.)     See  Lantern. 

LuFFES  Boarding.    The  same  as  blind  slats. 

Machicolations,  (in  Gothic  architecture,)  small  openings  in  an  em- 
battled parapet,  for  the  discharge  of  missile  weapons  upon  the  assail- 
ants. Frequently  these  openings  are  underneath  the  parapet ;  in 
which  case,  the  whole  is  brought  forward  and  supported  by 
corbels. 

SIechanical  Cabpentrt.  That  branch  of  earpentiT  which  teaches 
the  disposition  of  the  timbers  according  to  their  relative  strength, 
and  the   strains  to  which  they  ai-e  subjected. 

Mediaeval  AKcniTECTUEE.  The  architecture  of  England,  France, 
Germany,  &c.,  during  the  middle  ages,  including  the  Norman  and 
early  Gothic  styles. 

Members.  (Jicmfiriini,  Lat.)  The  different  parts  of  a  building;  the 
different  parts  of  an  entablature ;  the  different  mouldings  of  a  cor- 
nice, &c. 

Metope.  The  square  space  between  two  triglyphs  of  the  Doric  order. 
It  is  sometimes  left  plain,  at  other  times  decorated  with  sculpture. 

Mezzanine.    A  low  story  introduced  between  two  principal  stories. 

Minerva  Polias.    A  Grecian  temple  at  Athens. 

Minute.  The  sixtieth  part  of  the  diameter  of  a  column.  It  is  the 
subdivision  by  which  architects  measure  the  small  parts  of  an  order. 

Mitre.    An  angle  of  forty-five  degrees ;  a  half  of  a  right  angle. 

Modillion.  An  ornament  in  the  entablature  of  richer  orders,  resem- 
bling a  bracket. 

Module.  The  semi-diameter  of  a  column.  This  term  is  only  prop- 
erly used  when  speaking  of  the  orders.  As  a  semi-diameter,  it  con- 
sists of  only  thirty  minutes.     See  Minute. 

Mosaic.  A  kind  of  painting  representing  cubes  of  glass,  &c.,  and  is 
formed  of  different  colored  stones,  for  paving,  &c.  Specimens  of 
this  kind  have  been  found  among  the  ruins  of  antiquity. 

Mouldings.  Those  parts  of  an  order  which  are  shaped  into  various 
curved  or  square  foiins. 

Mouth.    The  same  as  Cavetto,  which  see. 


175 


MuTULE.    A  projecting  ornament  of  the  Doric  cornice,  which  occu 

pies  the  place  of  the  modillion,  in  imitation  of  the  ends  of  rafters. 
MuLLiON,  (in  Gothic  architecture,)  the  framework  of  a  window. 

Naked.    The  unornamcntcd,  plain  surface  of  a  wall,  column,  or  other 

part  of  a  building. 
Naos,  or  Cella.    The  part  of  a  temple  within  the  walls. 
Newel.     The  solid,  or  imaginaiy  solid,  when  the  stairs  are  open  in 

the  centre,  round  which  the  stops  are  turned  about. 
Niche.     A  square  or  cylindrical  cavity  in  a  wall  or  other  solid. 

Obelisk.  A  tall,  slender  frustum  of  a  pyramid,  usually  placed  on  a 
pedestal.  The  difference  between  an  obelisk  and  a  pyramid,  inde- 
pendent of  the  former  being  only  a  portion  of  the  latter,  is,  that  it 
always  has  a  small  base  in  proportion  to  its  height. 

Octastyle.    a  building  with  eight  columns  in  front. 

Ogee,  or  Ogive.    The  same  as  Cijma,  which  see. 

Order.  An  assemblage  of  parts,  consisting  of  a  base,  sh.-vft,  capital, 
architrave,  frieze,  and  cornice,  whose  several  services,  requiring  some 
distinction  in  strength,  have  been  contrived  or  designed  in  five  sev- 
eral species  —  Tuscan,  Doric,  Ionic,  Corinthian,  and  Composite; 
each  of  which  has  its  ornaments,  as  well  as  general  fabric,  propor- 
tioned to  its  strength  and  character. 

Oedonnance.  The  aiTangement  of  a  design,  and  the  disposition  of 
its  several  parts. 

Oele.  (Ttal.)  A  fillet  or  band  under  the  ovolo  of  the  capital.  Pal- 
ladio  applies  the  term  also  to  the  plinth  of  the  base  of  a  column  or 
pedestal. 

OvoLO.  A  moulding  sometimes  called  a  quarter  round,  from  its  pro- 
file, being  the  quadrant  of  a  circle.  When  sculptured,  it  is  called  an 
echinus,  which  see. 

Panel.    A  thin  board,  having  all  its  edges  inserted  in  the  groove  of  a 

suiTounding  frame. 
Paeapet.    From   the  Italian  Parapetto,  breast    high.     The  defence 

round  a  terrace  or  roof  of  a  building. 
Pakastat^.    Pilasters  standing  insulated. 

Pavilion.    A  tuiTet  or  small  building  generally  insulated,  and  com- 
prised beneath  a  single  roof. 
Pedestal.    The  substruction  under  a  column  or  wall.    A  pedestal 

under  a  column  consists  of  three  parts  —  the  base,  the  die,  and  the 

cornice  or  cap. 
Pediment.     The  low,  triangular,  crowning  ornament  of  the  front  of 

a  building,  or  of  a  door,  window,  or  niche. 
Pend,  (in  Gothic  architecture,)  a  vaulted  roof  without  groining. 
Pendant,  (in  Gothic  architecture,)  a  hanging  ornament  in  highly- 
-  enriched  vaulted  roofs. 

Pinnacle,  (in  Gothic  architecture,)  a  small  spire. 
Peripteral.    A  term  used  by  the  ancients  to  express  a  building 

encompassed  by  columns,  forming,  as  it  were,  an  aisle  round  the 

building. 
Peristylium.    In   Greek  and  Roman  houses,  a  com't,  square,  or 

cloister. 
Perspective  is  the  science  which  teaches  us  to  dispose  the  lines  and 

shades  of  a  picture,  so  as  to  represent,  on  a  plane,  the  image  of  ob- 
jects exactly  as  they  appear  in  nature. 
Piazza.    A  continued  archway,  or  vatilting,  supported  by  pillars  or 

columns ;  a  portico. 
Pier.    A  solid  between  the  doors  or  the  windows  of  a  buildjng.    Tie 

square  or  other  formed  mass  or  post  to  which  a  gate  is  hung. 
Pilaster.    A  square  pillar  engaged  in  a  wall. 
Pile.    A  stake  or  beam  of  timbers,  driven  firmly  into  the  ground. 
Pillar.    A  column  of  irregular  form,  always  disengaged,  and  always 


176 


GLOSSARY  OF  ARCHITECTURAL  TERMS. 


deviating  from  the  proportions  of  tlie  orders  ;  whence  tlie  distinction 
between  a  pillar  and  a  column. 

Platband.  A  square  moulding,  whose  projection  is  less  than  its 
height  or  breadth. 

Plinth.  The  square  solid  laider  the  base  of  a  column,  pedestal,  or 
wall. 

PoKcn.  An  arched  vestibule  at  the  entrance  of  a  church  or  other 
building. 

Portico.  A  place  for  walking  under  shelter,  raised  with  arches  in  the 
manner  of  a  gallei7  ;  the  portico  is  usually  vaulted,  but  has  some- 
times a  flat  soffit  or  ceiling.  This  word  is  also  used  to  denote  the 
projection  before  a  church  or  temple  supported  by  columns. 

Post.  A4)iece  of  timber  set  erect  in  the  earth.  Perpendicular  tim- 
bers of  the  wooden  frame  of  a  building. 

PoSTicnJi.  The  back  door  of  a  temple ;  also  the  portico  behind  the 
temple. 

PiiiNCiPAL  Eaftees.  The  two  inclined  timbers  which  support  the 
roof 

Peofile.    The  contour  of  the  different  parts  of  an  order. 

Peojecture.  The  prominence  of  the  mouldings,  and  members  be- 
yond the  naked  surface  of  a  column,  wall,  &c. 

Proscenium.  The  front  part  of  the  stage  of  the  ancient  theatres,  on 
which  the  actors  performed. 

Prostyle.    A  building  or  temple  with  columns  in  front  only. 

PuELiNS.  Pieces  of  timber  framed  horizontally  from  the  principal 
rafters,  to  keep  the  common  rafters  from  sinking  in  the  middle. 

PvcNOSTTLB.  An  intercolumniatiou  equal  to  one  diameter  and 
a  half. 

Pyramid.  A  solid,  with  a  square,  polygonal,  or  triangular  base,  ter- 
minating in  a  point  at  top. 

Quarter  Eound.    See  Ocolo  and  Echinus. 

QuATEEFOiL,  (in  Gothic  architecture,)  an  ornament  in  tracery,  con- 
sisting of  four  segments  of  circles,  or  cusps,  within  a  circle. 

Quirk  Mouldings.  The  convex  part  of  Grecian  mouldings,  when 
they  recede  at  the  top,  forming  a  rcOnticcnt  angle  with  the  surface 
which  covers  the  moulding. 

Quoins.  The  external  and  internal  angles  of  buildings,  or  of  their 
members.    The  corners. 

Radius,  in  geometry,  is  the  semi-diameter  of  a  circle,  or  a  right  line, 

drawn  from  the  centre  to  the  circumference  ;  in  mechanics,  the  spoke 

of  a  wheel. 
Rails,  in  framing,  the  pieces  that  lie  horizontal  j  and  the  perpendicu- 
lar pieces  are  called  styles,  in  wainscoting,  &c. 
Raking.    A  term  applied  to  mouldings  whose  arrises  are  inclined  to 

the  horizon. 
Resistance,  in  mechanics,  that  power  which  acts  in  opposition  to 

another,  so  as  to  diminish  or  destroy  its  effect. 
Reticulated  Work.    That  in  which  the  courses  are  arranged  in  a 

net-like  form.    The  stones  arc  square,  and  placed  lozengewise. 
Return.    {Fr.)    The  continuation  of  a  moulding,  projection,  &c.,  in 

an  opposite  direction,  as  the  flank  of  a  portico,  &c. 
Rib.    (Sax.)    An  arched  piece  of  timber  sustaining  the  plaster  work 

of  a  vault,  &c. 
Ridge.    The  top  of  the  roof,  which  rises  to  an  acute  angle. 
Rilievo,  or  Relief.    The  projccture  of  an  architectural  ornament. 
Ring.    A  name  sometimes  given  to  the  list,  cincture,  or  fillet. 
Roman  Order.    Another  name  for  the  Composite. 
Rose.    The  representation  of  this  flower  is  carved  in  the  centre  of 

each  face  of  the  abacus  in  the  Corinthian  capital,  and  is  called  the 

rose  of  that  capital. 
Rustic.    The  courses  of  stone  or  brick,  in  which  the  work  is  jagged 


out   into   an    irregular   surface.      Also,    work    left    rough   without 
tooling. 

Sagging.  The  bending  of  a  body  in  tlio  middle  by  its  own  weight, 
when  suspended  horizontally  by  each  end. 

Salon.  [Fr.)  An  apartment  for  state,  or  for  the  reception  of  paint- 
ings, and  usually  running  up  through  two  stories  of  the  house.  It 
may  be  square,  oblong,  polygonal,  or  circular. 

Saloon.  A  lofty  hall,  usually  vaulted  at  the  top,  with  two  stages 
of  windows. 

Sash.     The  wooden  frame  which  holds  the  glass  in  windows. 

Scaffold.  A  frame  of  wood  fixed  to  walls,  for  masons,  plasterers, 
&c.,  to  stand  on. 

Scantling.  The  name  of  a  piece  of  timber,  as  of  quartering  for  a 
partition,  when  under  five  inches  square,  or  the  rafter,  purlin,  or  pole- 
plate  of  a  roof. 

ScAPUS.    Tlie  same  as  Shaft  of  a  column,  which  see. 

Scarfing.  The  .joining  and  bolting  of  two  pieces  of  timber  together 
transversely,  so  that  the  two  appear  but  as  one. 

Scotia.  The  name  of  a  hollowed  moulding,  principally  used  between 
the  tori  of  the  base  of  columns. 

Severy,  (in  Gothic  architecture,)  a  separate  portion  of  a  building. 

SnAFT.  That  part  of  a  column  which  is  between  the  base  and  capital. 
It  is  also  called  the/Hs(,  as  well  as  trmd;  of  a  column. 

Shank.  A  name  given  to  the  two  intcrstical  spaces  between  the 
channels  of  the  triglyph  in  the  Doric  frieze. 

Shooting.  Planing  the  edge  of  a  board  straight,  and  out  of 
winding. 

Shoulder.  The  ])lane,  transverse  to  the  length  of  a  piece  of  timber 
from  which  a  tenon  projects. 

Shutters.  The  boards  or  wainscoting  which  shut  up  the  aperture  of 
a  window. 

Sill.  The  timber  or  stone  at  the  foot  of  a  window  or  door;  the 
ground  timbers   of  a  frame  wbicli  support  the  posts. 

Skirtings.  The  narrow  boards  which  form  a  plinth  round  the  mar- 
gin of  a  floor. 

Socle.  A  square,  flat  member,  of  greater  breadth  than  height,  usu- 
ally the  same  as  plinth. 

Soffit.  The  ceiling  or  under  side  of  a  member  in  an  order.  It 
means  also  the  under  side  of  the  larmier  or  corona  in  a  cornice ; 
also,  the  under  side  of  that  part  of  the  architrave  which  does  not  rest 
on  the  columns.     Sec  also  Lacunar. 

SoMMER.  The  lintel  of  a  door,  window,  &c. ;  a  beam  tenoned  into  a 
girder,  to  support  the  ends  of  joists  on  both  sides  of  it. 

Spandrel,  (in  Gothic  architecture,)  the  triangular  space  enclosed  by 
one  side  of  an  arch,  and  two  lines  at  right  angles  to  each  other;  one 
horizontal,  and  on  a  level  with  the  apex  of  the  arch,  the  other  per- 
pendicular, and  a  continu.ition  of  the  line  of  the  jamb. 

Spiral.  A  curve  line  of  a  circular  kind,  which  in  its  progress  recedes 
from  its  centre. 

Steps.    The  degrees  in  ascending  a  staircase. 

Stereobata,  or  Stylobata.     The  same  as  Entasis. 

Strap.  An  iron  plate,  to  secure  the  junction  of  two  or  more  timbers, 
into  which  it  is  secured  by  bolts. 

Stretching  Course.  Bricks  or  stones  laid  in  a  wall,  with  their 
longest  dimensions  in  the  horizontal  line. 

SuRBASE.     The  mouldings  immediately  above  the  base  of  a  room. 

Systyle.    An  intercolumniatiou  equal  to  two  diameters. 

Table,  (in  Gothic  architecture,)  any  surface,  or  flat  member. 

TiENi.    A  term  usually  applied  to  the  lastel  above  the  architrave  in 

the  Doric  corder. 
Templet.    A  mould  used  by  bricklayers  and  masons  for  cutting  or 


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